Undergraduate Courses in Physics ...... 1 1.1 INTRODUCTION ...... 1 1.2 PHYSICS COURSES IN THE ACADEMIC YEAR 2013-14 ...... 1 1.2.1 The First Year (Part IA) ...... 1 1.2.2 The Second Year (Part IB) ...... 2 1.2.3 The Third Year (Part II) - Physics ...... 2 1.2.4 The Fourth Year (Part III) - Physics ...... 3 1.2.5 Master of Advanced Studies (MASt) in Physics ...... 3 1.3 MATHEMATICS AND THE PHYSICS COURSES ...... 3

Aims and Objectives of the Physics Teaching ...... 4

Programme ...... 4 2.1 THE UNIVERSITY’S AIMS AND OBJECTIVES ...... 4 2.2 COURSE AIMS ...... 4 2.3 COURSE OBJECTIVES ...... 4

Part IA Physics ...... 6 3.1 AIMS OF THE COURSE ...... 6 3.2 THE LECTURE COURSES ...... 6 3.3 PRACTICALS ...... 6 3.4 THE EXAMINATION ...... 6 3.4.1 Examiners’ Notices ...... 6 3.4.2 The Written Paper for Part IA...... 6 3.5 BOOKS ...... 6 3.6 SOME IMPORTANT DATES ...... 8 3.7 LECTURE LIST ...... 9 PRINCIPLES OF CLASSICAL PHYSICS, QUANTUM PHYSICS & RELATIVITY ...... 10 IA PRACTICAL CLASS ...... 13

Part IB Physics A ...... 15 4.1 INTRODUCTION AND COURSE AIMS ...... 15 4.2 THE CONTENT OF THE COURSE ...... 15 4.3 THE EXAMINATION ...... 15 4.4 SOME IMPORTANT DATES ...... 16 4.5 LECTURE LIST ...... 17 EXPERIMENTAL METHODS ...... 18 OSCILLATIONS, WAVES AND OPTICS ...... 19 QUANTUM PHYSICS ...... 20 CONDENSED MATTER PHYSICS ...... 22 MATHEMATICAL METHODS ...... 23 GREAT EXPERIMENTS...... 24 IB PRACTICAL CLASS – PHYSICS A ...... 25

Part IB Physics B ...... 26 5.1 INTRODUCTION AND COURSE AIMS ...... 26

5.2 COURSE CONTENT ...... 26 5.3 THE EXAMINATION ...... 26 5.4 SOME IMPORTANT DATES ...... 27 5.5 LECTURE LIST ...... 28 ELECTROMAGNETISM ...... 29 CLASSICAL DYNAMICS ...... 31 THERMODYNAMICS ...... 32 INTRODUCTION TO COMPUTING ...... 33 MATHEMATICAL METHODS ...... 35 GREAT EXPERIMENTS ...... 36 IB PRACTICAL CLASS – PHYSICS B ...... 37 IB PRACTICAL CLASS – PHYSICS A and B ...... 38

Part II Physics ...... 42 6.1 THE THREE- AND FOUR-YEAR COURSES IN PHYSICS ...... 42 6.2 OUTLINE OF THE COURSES ...... 42 6.3 FURTHER WORK ...... 43 6.3.1 Computing ...... 43 6.3.2 Experimental Investigations ...... 43 6.3.3 Courses in Theoretical Physics ...... 43 6.3.4 Research Review ...... 45 6.3.5 Long-Vacation Work ...... 45 6.3.6 Physics Education...... 45 6.4 SUPERVISIONS AND EXAMPLES CLASSES ...... 45 6.5 NON-EXAMINED WORK ...... 46 6.6 THE EXAMINATION ...... 46 6.6.1 Examiners’ Notices ...... 46 6.6.2 The Written Papers for Part II ...... 46 6.6.3 Requirements ...... 46 6.6.4 Examination Entries...... 46 6.6.5 Submission of Further Work ...... 46 6.7 HALF SUBJECT PHYSICS ...... 47 6.8 SOME IMPORTANT DATES ...... 48 6.9 LECTURE LIST ...... 49 ADVANCED QUANTUM PHYSICS ...... 50 OPTICS AND ELECTRODYNAMICS ...... 51 RELATIVITY ...... 52 THERMAL AND STATISTICAL PHYSICS ...... 54 ASTROPHYSICAL FLUID DYNAMICS ...... 55 PARTICLE AND NUCLEAR PHYSICS ...... 57 QUANTUM CONDENSED MATTER PHYSICS ...... 59 SOFT CONDENSED MATTER ...... 60 COMPUTATIONAL PHYSICS ...... 61 COMPUTATIONAL PHYSICS PROJECT ...... 62 THEORETICAL PHYSICS 1 - CLASSICAL FIELD THEORY (TP1) ...... 63 THEORETICAL PHYSICS 2 - TOPICS IN QUANTUM THEORY (TP2) ...... 65 PART II EXPERIMENTS ...... 66 RESEARCH REVIEWS ...... 69 PHYSICS EDUCATION ...... 71 CONCEPTS IN PHYSICS ...... 73

Part III Physics ...... 75 7.1 INTRODUCTION...... 75 7.2 MASTER OF ADVANCED STUDIES (MAST) IN PHYSICS ...... 75 7.3 OUTLINE OF THE COURSE ...... 75 7.4 DETAILS OF THE COURSES...... 76

7.4.1 Project work ...... 76 7.4.2 Major Topics...... 76 7.4.3 Minor Topics ...... 76 7.4.4 Other Lent Term courses ...... 77 7.4.5 Further Work ...... 77 7.4.6 Long-Vacation Projects ...... 77 7.4.7 Entrepreneurship ...... 77 7.4.8 Examples Class in General Physics ...... 77 7.5 RESTRICTIONS ON COMBINATION OF COURSES ...... 78 7.6 SUPERVISIONS ...... 78 7.7 NON-EXAMINED WORK ...... 78 7.8 THE EXAMINATION ...... 78 7.8.1 Examiners’ Notices ...... 78 7.8.2 Examination Entries ...... 78 7.8.3 The Written Papers for Part III ...... 78 7.9 SOME IMPORTANT DATES ...... 81 7.10 LECTURE LIST ...... 83 ADVANCED QUANTUM CONDENSED MATTER PHYSICS ...... 84 ATOMIC AND OPTICAL PHYSICS ...... 85 PARTICLE PHYSICS ...... 86 PHYSICS OF THE EARTH AS A PLANET ...... 88 QUANTUM CONDENSED MATTER FIELD THEORY ...... 90 QUANTUM FIELD THEORY ...... 91 RELATIVISTIC ASTROPHYSICS AND COSMOLOGY ...... 92 SOFT MATTER AND BIOLOGICAL PHYSICS ...... 94 ATMOSPHERIC PHYSICS ...... 95 BIOLOGICAL PHYSICS ...... 96 FORMATION OF STRUCTURE IN THE UNIVERSE ...... 97 GAUGE FIELD THEORY ...... 99 MEDICAL PHYSICS ...... 100 NONLINEAR OPTICS AND QUANTUM STATES OF LIGHT ...... 102 PARTICLE ASTROPHYSICS ...... 103 SUPERCONDUCTIVITY AND QUANTUM COHERENCE ...... 104 THE FRONTIERS OF OBSERVATIONAL ASTROPHYSICS ...... 105 QUANTUM INFORMATION ...... 107 ADVANCED QUANTUM FIELD THEORY ...... 108 NUCLEAR POWER ENGINEERING ...... 109 INTERDISCIPLINARY TOPICS – NST PART III ...... 111 MATERIALS, ELECTRONICS AND RENEWABLE ENERGY ...... 112 ENTREPRENEURSHIP ...... 113 ETHICS IN PHYSICS...... 115 PHILOSOPHY OF PHYSICS ...... 116 PROJECTS ...... 117

Guide for Students ...... 123 Academic Staff ...... 125 Administration ...... 126 Aims and Objectives ...... 126 Appeals ...... 126 Astronomical Society (CUAS) ...... 126 Bicycles ...... 126 Books ...... 126 Bookshops ...... 126 Buildings ...... 127 Calculators ...... 127 CamCORS ...... 127 CamSIS ...... 127

CamTools ...... 127 Canteen ...... 127 Careers ...... 127 Cavendish Laboratory ...... 127 Cavendish Stores ...... 127 Cheating ...... 127 Classing Criteria ...... 128 College ...... 128 Common Room ...... 128 Complaints ...... 128 Computing ...... 128 Counselling ...... 129 Courses ...... 129 Databases ...... 129 Department of Physics ...... 129 Director of Studies ...... 130 Disability ...... 130 Electronic Mail ...... 130 Examinations ...... 130 Examples Classes ...... 131 Examples Sheets ...... 131 Faculty of Physics and Chemistry ...... 131 Feedback ...... 131 Fire Alarms ...... 131 Formulae ...... 131 Handbook ...... 132 Harassment ...... 132 Institute of Physics ...... 132 Laboratory Closure...... 132 Late Submission of Work ...... 132 Lecture handouts ...... 132 Lectures ...... 133 Libraries ...... 133 MASt ...... 133 Managed Cluster Service (MCS – formally PWF) ...... 133 Moore Library ...... 133 Natural Sciences Tripos ...... 133 Part II and Part III Library ...... 134 Past Tripos papers ...... 134 Personal Computers ...... 134 Philosophical Society ...... 134 Physics Course Handbook ...... 134 Photocopying ...... 134 Physics Society (CUPS) ...... 134 Plagiarism ...... 134 Practical Classes ...... 134 Rayleigh Library ...... 134 Raven ...... 135 Recording of Lectures ...... 135 Refreshments ...... 135 Registration ...... 135 Reporter ...... 135 Research ...... 135 Safety ...... 136 Scientific Periodicals Library ...... 136 Smoking ...... 136 Staff-Student Consultative Committee ...... 136 Supervisions ...... 136

Synopses ...... 136 Teaching Committee ...... 137 Teaching Information System ...... 137 Teaching Office ...... 137 Telephones ...... 137 Transferable Skills ...... 137 University Library ...... 137 World-Wide Web ...... 138

Web Site

This Physics Course Handbook and some of the references therein can be found on the Cavendish Laboratory World-Wide Web teaching pages at http://www.phy.cam.ac.uk/teaching/.

Teaching Office

The Cavendish Laboratory’s Teaching Office is situated in the Bragg Building, Room 212B. Opening times during full term will be posted outside the office. Enquiries can also be made via the e-mail address [email protected].

Undergraduate Courses in Physics

1.1 INTRODUCTION four-year courses. Synopses for all the courses to be delivered in the academic year 2013-14 are in- The Department of Physics in Cambridge offers cluded in this booklet. both three and four year courses in physics, which The aims and outcomes for the courses can be form the two basic routes to a first degree with found through the course web site located at specialisation in physics. The four-year course is http://www.phy.cam.ac.uk/teaching designed for students who wish to pursue a professional career in physics, for example, in aca- 1.2 PHYSICS COURSES IN THE demic or industrial research: it leads to an ACADEMIC YEAR 2013-14 honours degree of Master of Natural Sciences, M.Sci., together with an honours degree Bachelor In this section we give a brief overview of the of Arts, B.A. The three year course is designed for courses offered; fuller details are given in the in- students with a deep interest in the subject but troduction to each year below. who may not intend to become professional physicists: it leads to an honours degree of B.A. 1.2.1 The First Year (Part IA) Physics graduates from Cambridge go in a wide Students in the first year of the Natural Sciences range of directions. Nearly half embark on re- Tripos (NST) choose three experimental subjects search leading to a higher degree, and about a with a free choice from Physics, Chemistry, Mate- quarter go straight into full-time employment in a rials Science, Earth Sciences, Biology of Cells, wide variety of fields, such as teaching, business Evolution and Behaviour, and Physiology of Or- and finance, and computing. The remainder are ganisms. In addition, all NST students reading spread over other types of postgraduate activities. Physics will take the NST Mathematics course. Our graduates have an excellent record of finding Paper 1 of Part IA of the Computer Science Tripos employment promptly after graduation. may be substituted for Biology of Cells. As regards research towards a Ph.D., at present The Physics course assumes either A2 level Phys- the policy announced by the UK Research Coun- ics (or equivalent), or A2 level Further Maths (in- cils is that an Upper Second or First Class in ei- cluding the Mechanics modules). Ideally students ther the third or fourth years formally qualifies a would have done both Physics and Further Maths, student for a Ph.D. award. However, the policy of but this is definitely not essential. this Department and many others is that Part III The first-year course, Part IA Physics, covers fun- is an essential preparation for a Ph.D. damental principles in physics. The aim is to In both the three and four year courses our aims bridge the gap between school and university are to provide a solid foundation in all aspects of physics by providing a more complete and logical physics and to show something of the very broad framework in key areas of classical physics, as well spectrum of modern physics. Vital basic areas as introducing new areas such as relativity and such as Electromagnetism, Quantum Mechanics, quantum physics. The Part IA Physics course is Dynamics and Thermodynamics are covered in given in three lectures per week plus a four-hour the first three years, where we also aim to develop experiment once every two weeks. Subjects stud- experimental, computational and mathematical ied include Mechanics, Relativity, Oscillations and skills. Advanced work in the fourth year can in- Waves, Quantum Waves, and Fields. clude fundamental subjects such as Advanced The first-year physics course is also available in Quantum Theory, Particle Physics, Condensed Part IA of the Computer Sciences Tripos, where it Matter Physics and Cosmology as well as applied is combined with courses in Mathematics for topics such as Biological Physics and Geophysics. Natural Sciences and Computer Science Courses. A substantial piece of independent project work is It is also possible to read Part IA Physics as part of required in the fourth year, and there are also the Mathematical Tripos in the first-year course possibilities for experience of industrial research ‘Mathematics with Physics’. Both of these routes during the long vacations. provide for possible specialisation in physics in In the following sections, brief descriptions are later years. given of the undergraduate courses currently of- There is no limit on numbers and we usually have fered by the department. The flow chart inside the about four hundred students reading Part IA front cover shows routes through the three- and Physics. 1.2.2 The Second Year (Part IB) Physics. Further, the practical work draws heavily on material presented in Physics A in the There are two physics courses in Part IB: Physics Michaelmas Term: students taking just Physics B A and Physics B. Physics A provides a grounding are advised to attend the Experimental Methods in quantum mechanics and solid-state physics, lectures for Physics A for necessary background. while Physics B covers the core of classical phys- We expect that the majority of students wishing to ics, including electromagnetism, dynamics and pursue a single physics course will find IB Physics thermodynamics. A the more attractive option. The combination of IB Physics A and Physics B offers a firm grounding in key areas of physics - theoretical and experimental - and covers special- 1.2.3 The Third Year (Part II) - ised topics that lead naturally to Part II/III Phys- Physics ics and other quantitative subjects. Students The aim of the third-year Part II Physics course is taking both courses combine them with one other to complete instruction in core physics and to be- IB subject. This third subject is often NST IB gin to introduce more advanced topics required Mathematics, and this is useful for students wish- for a professional career in research. The available ing to pursue theoretical options in Part II. How- courses cover a broad range of experimental, ever, choosing a different subject provides theoretical and computational subjects, with an additional breadth and gives greater choice of Part element of choice that allows students to explore II and Part III courses. Common choices for the topics they find particularly interesting and, if third subject are Materials Science, Chemistry A, they wish, to concentrate on more experimental or Geology A or History and Philosophy of Science. theoretical work. Professional skills are developed For students taking either Physics A or Physics B through lectures, example classes, computing ex- without NST IB Mathematics, additional lectures ercises and extended experiments, depending on in Mathematical Methods are provided within the the courses taken. course. In the Michaelmas term, there are core courses in There is no limit on the number of students taking Advanced Quantum Mechanics, Relativity, Optics IB Physics A and Physics B; usually about 170 stu- and Electrodynamics and Thermal and Statistical dents take both. Most proceed into Part II Phys- Physics. ics, but some go into other third-year science subjects or into other triposes. In the Lent and Easter term, students have some choice amongst lecture courses including Astro- Students come into the combination of IB Physics physical Fluid Dynamics, Particle and Nuclear A and B mostly having taken both Physics and Physics, Quantum Condensed Matter, and Soft Mathematics in Part IA of the Natural Sciences or Condensed Matter. Additionally there is a short Computer Sciences Triposes. Of those who have course on Computational Physics, with associated taken the first-year Mathematics with Physics (compulsory) exercises, and a short, more general course in the Mathematics Tripos, a significant course on Concepts in Physics. proportion subsequently take IB Physics A and B. Students are also required to submit three or A smaller number of students, usually ten to more items of Further Work. You may choose an twenty, take IB Physics A as their only physics experimentally-biased course or one with a course. IB Physics A provides a self-contained stronger emphasis on theory, or some intermedi- package of quantum, condensed matter and ex- ate combination of experiment and theory. For perimental physics. It builds on IA Physics and of- example, there is the option of carrying out up to fers a firm grounding in important areas of two experimental investigations, each lasting two physics that is very useful for scientists with a weeks. For theorists, there are two courses in wide range of career destinations. The students Theoretical Physics, consisting of lectures plus ex- will normally take two other Part IB subjects, and amples classes, which run through the Michael- then go into a wide range of third-year courses. mas and Lent terms. Other possible units of Note that Part IB Physics A alone is not an ade- Further Work include: the Computational Physics quate preparation for Part II Physics. project, assessed Long Vacation work, the Physics It is also possible for students to take IB Physics B Education course and a Research Review. as their only physics course, and this may suit There is no limit on the number of students taking students with a particular interest in the topics Part II Physics and we usually have about 120 covered in that course. Note that Part IB Physics students, the largest class in any Part II Natural B alone is not an adequate preparation for Part II Science subject. Undergraduate Courses in Physics 2 An alternative for the third year is Half Subject 1.2.5 Master of Advanced Studies Physics in Part II Physical Sciences of the Natural (MASt) in Physics Sciences Tripos. This is offered to students who wish to retain an interest in physics but to keep This is a taught postgraduate course, which con- other options open at the same time. They select sists of the same content as Part III Physics. This about half the workload from the third-year phys- course is designed for students who hold a 3-year ics course, combined with a Part IB subject which undergraduate degree who wish to pursue a re- they have not previously taken, such as History search degree. The entry requirement for the and Philosophy of Science plus a Dissertation. We MASt is a qualification comparable to an upper expect that students offering Half Subject Physics second class or better UK Bachelor’s degree in will have read IB Physics A or Physics B in the Physics. second year. Advice on suitable combinations of Part II Physics courses can be obtained from your 1.3 MATHEMATICS AND THE Director of Studies. PHYSICS COURSES 1.2.4 The Fourth Year (Part III) - The mathematical skills needed by students who Physics follow the three or four-year physics course are quite varied. Students taking entirely experimen- The fourth-year course, Part III Physics, is de- tal options may need much less sophisticated signed to provide the necessary foundation for a mathematics than those taking the more advanced professional career in academic or industrial re- theoretical options. The level of mathematics search. The course spans the spectrum from preparation at school is also variable. Some stu- strongly experimental to highly theoretical physics dents entering Part IA Physics have studied two and offers the flexibility for students to select a A2-levels in Mathematics and others have studied wide range of different combinations of subjects, only one A2-level. according to their career aspirations. Many of the The aim of the Physics Department is to challenge courses reflect major research interests of staff of the most gifted and best-prepared students, while the Cavendish. There is a substantial amount of providing access to theoretical courses for those independent project work, which may be pro- less well prepared. The Mathematics course for posed by the students themselves, together with Natural Scientists In Part IA assumes only single opportunities to include work in external labora- Mathematics A2-level. tories and industry through assessed vacation projects. In the second year, both IB Physics courses assume only mathematical material from NST IA Our aim in the fourth year is to present physics as mathematics. Other necessary mathematical a connected subject of enormous flexibility and techniques are taught alongside the physics or in applicability. Revision classes in general physics Part IB Mathematics: for those not taking are given in the Easter Term and all students un- Mathematics in Part IB, there is a non-examined dertake a substantial project which is worth one (but supervised) course in Mathematical Methods third of the years marks. Lecture courses in the given in the Michaelmas Term. This covers all the first and second terms provide more advanced mathematical material needed for the Part II core treatments of major areas of physics and are se- and options courses. lected to reflect broad areas of current interest. Many of them have an interdisciplinary character. The optional theoretical courses in Part II prepare The overall course provides excellent preparation students for the theoretical options in Part III. for a research career inside or outside physics in Students intending to take TP1 and/or TP2, and either the academic or industrial sectors. who have not taken Part IB NST Mathematics, will find it helpful to do some extra preparation in the long vacation at the end of Part IB.

Undergraduate Courses in Physics 3 Aims and Objectives of the Physics Teaching Programme

2.1 THE UNIVERSITY’S AIMS AND • To provide an intellectually stimulating environment in which students have the opportu- OBJECTIVES nity to develop their skills and enthusiasms to The Quality Assurance Agency, through its institu- the best of their potential; tional audit of the University, is concerned with • To maintain the highest academic standards in the assurance of the quality of teaching and learn- undergraduate and graduate teaching and to ing within the University. The University in turn develop new areas of teaching and research in requires every Department to have clear aims and response to the advance of scholarship and the objectives and to monitor their teaching and needs of the community. learning activities and consider changes where necessary. Students should be aware of these 2.3 COURSE OBJECTIVES Aims and Objectives, which have been the subject of considerable discussion within the Department, By the end of the first year (Part IA Physics), with the University and with the Physics Staff- students, whether continuing with physics or not, Student Consultative Committee. If you have any should have: comments on the Aims and Objectives of the • attained a common level in basic mathemati- Physics Teaching Programme, which are printed cally-based physics, and so laid a secure foun- below, please contact Dr John Richer, Director of dation in physics for their future courses Undergraduate Teaching, Cavendish Laboratory. within the Natural Sciences or other Triposes; The University’s stated aims are ‘to foster and de- • acquired a broad introduction to a range of sci- velop academic excellence across a wide range of ences at University level, generally through subjects and at all levels of study’. Furthermore, having studied two other experimental sub- the University aims ‘to provide an education of the jects as well as mathematics; highest calibre at both the undergraduate and postgraduate level, and so produce graduates of • developed their experimental and data analysis the calibre sought by industry, the professions, skills through a wide range of experiments in and the public service, as well as providing aca- the practical laboratories. demic teachers and researchers for the future’. By the end of the second year, students tak- The broad aims of the Department of Physics are ing Part IB Physics A and Physics B should identical with these. have: In the context of the Departmental teaching pro- • been introduced to powerful tools for tackling grammes, the specific aims and objectives are a wide range of topics, including formal meth- given below. ods in classical and quantum physics; 2.2 COURSE AIMS • become familiar with additional relevant mathematical techniques; • To provide education in physics of the highest quality at both the undergraduate and gradu- • further developed their experimental skills ate levels and so produce graduates of the cali- through a series of whole-day experiments, bre sought by industry, the professions, and some of which also illustrate major themes of the public service, as well as providing the aca- the lecture courses, and developed their com- demic teachers and researchers of the future; munication skills through group activities. • To encourage and pursue research of the high- By the end of the second year, students tak- est quality in physics, and maintain Cam- ing Part IB Physics A should have: bridge’s position as one of the world’s leading • covered a wide range of topics in quantum and centres in these fields; condensed matter physics with emphasis upon • To continue to attract outstanding students their practical applications and utility; from all backgrounds; • further developed their practical skills through a series of whole-day experiments, some of which illustrate major themes of the lecture courses. 4 Aims and Objectives By the end of the second year, students tak- • had experience of independent work . ing Part IB Physics B should have: By the end of the third year, students taking Half • covered a range of topics in classical physics, Subject Physics in Part II Physical Sciences including electromagnetism, dynamics and should have: thermodynamics; • enhanced their understanding of core physics, • further developed their practical skills through in the context of a broader exposure to science a series of whole-day experiments, some of with the Natural Sciences Tripos; which illustrate major themes of the lecture • had some experience of independent work. courses.

• have been introduced to scientific computing using the C subset of the C++ language. By the end of the fourth year (Part III Phys- ics), students completing the four-year option By the end of the third year (Part II Physics), should have: students taking Part II PHYSICS should have: • had experience of a number of broad areas of physics from a choice of options, taken to an • completed their study of core physics; advanced level, at which current research can • substantially developed professional skills in be appreciated in some depth; experimental and/or theoretical and/or com- • carried out a substantial independent research putational physics, or in Physics Education; project amounting to the equivalent of about • had experience of independent work, including six weeks of full-time work; an introduction to aspects of research; • maintained their skills in core physics; • had experience of the application of computers • enhanced their communications skills; to physical problems; • become well prepared for a career in academic • developed their communication skills or industrial research.

Aims and Objectives 5 Part IA Physics

Comments may be sent to [email protected] Enquiries/queries: [email protected]

3.1 AIMS OF THE COURSE you practice in technical writing you are required to do two formal reports. The first, partial, report, An important objective of the course is to develop to be written over the Christmas vacation, will be an understanding of ‘core physics’ at successively based on one of the experiments carried out over deeper levels, each stage revealing new phenom- the Michaelmas term. The second, to be written ena and greater insight into the behaviour of mat- over the Easter vacation, will be a full report on ter and radiation. one of the Lent-term experiments. Full details are The first year of the course has several distinct given in your practical class manual, and tips and aims. First, it aims to bridge the gap between further advice is given in the booklet entitled school- and university-level physics, and to bring Keeping Laboratory Notes and Writing Formal students from different backgrounds to a common Reports, which is handed out to students at the point. Second, it aims to consolidate school phys- start of the year. The overall practical mark ics by providing a much more logical and analyti- counts 25% towards the Part IA Physics examina- cal framework for classical physics, which will be tion. Around a third of the practical mark comes essential for all years of the course. Third, it in- from the Formal reports. cludes new themes such as special relativity and 3.4 THE EXAMINATION quantum physics, which foreshadow key topics to be developed in the subsequent years of the 3.4.1 Examiners’ Notices course. Fourth, the individual lecture courses aim to broaden your perspective, so that you can begin Specific information about the examination is to appreciate the great flexibility and generality of given in notices put up in a special Examinations the laws of physics and their application. section of the notice board inside the Part IA Prac- tical class. There is an introductory talk at 11.00 am on the first Wednesday of Michaelmas full term 3.4.2 The Written Paper for Part IA (9th October 2013), at the Cavendish Labora- tory, in the Pippard Lecture Theatre. The Part IA Physics written examination consists of one three-hour paper. The exact content of the 3.2 THE LECTURE COURSES paper is a matter for the relevant examiners, but the expected pattern will consist of questions on Details of the lecture courses are given in the syn- general physics and the material covered in the opses which follow. All students attend the same lecture courses. Note that the Part IA syllabus lectures. was changed at the start of the academic 3.3 PRACTICALS year 2009-2010 and earlier examination papers will occasionally refer to topics Students attend a physics practical for one after- which are no longer taught. noon once every two weeks. The primary aim of the class is the development of experimental 3.5 BOOKS skills, which are important to all professional There are two books recommended for the IA physicists. A second aim of the practical session is Physics course – these will be available in College to illustrate ideas and concepts in physics. Some libraries. Lecturers will give references both to of the experiments are concerned with illustrating relevant sections of these books, and to worked topics covered in the Part IA Physics lecture examples in them, which help explain or expand course, but this is not their main purpose. on the material they present in their lectures. Registration and assignment of days for practicals Similarly, the question sheets may sometimes re- are dealt with centrally, via your College. You are fer to the examples in these books for students expected to do your practical on the same day of who wish to try additional problems. This is to en- the week in each term. The practicals are continu- courage you to develop your skills in utilising the ously assessed. In addition, to prepare for each more extensive resource material provided in text- practical you are asked to carry out a brief exercise books to deepen your understanding of physics. beforehand, which you will hand in to your demonstrator at the start of the practical class. To give 6 Part IA Physics [1] Understanding Physics (Second Edition), Mansfield M & O’Sullivan C (Wiley 2011)

[2] Physics for Scientists and Engineers (Ex- tended Version), Tipler P A & Mosca G (6th Edi- tion, Freeman 2008)

Part IA Physics 7 3.6 SOME IMPORTANT DATES

Note: This list is not exhaustive, and may be superseded by announcements on the TIS Tuesday 8th October 2013 Start of Michaelmas full term Wednesday 9th October 2013 11.00 Introductory talk and registration and assignment of days for practicals, at the Caven- dish Laboratory (Pippard Lecture Theatre) Thursday or 5th & 6th December 10.00-16.00 Pick up notebook and instructions for Friday 2013 formal report from IA Practical Class Friday 6th December 2013 End of Michaelmas full term Tuesday 14th January 2014 Start of Lent full term Tuesday or 14th & 15th January 10.00-16.00 Formal report must be handed in to Wednesday 2014 the IA Practical Class Thursday or 13th & 14th March 10.00-16.00 Pick up notebook and instructions for Friday 2014 formal report from IA Practical Class Friday 14th March 2014 End of Lent full term Tuesday 22nd April 2014 Start of Easter full term Tuesday or 22nd & 23rd April 10.00-16.00 Formal report must be handed in to Wednesday 2014 the IA Practical Class Friday 13th June 2014 End of Easter full term

Late Submission of Work In accordance with the University’s regulations, work submitted after the advertised deadline will not count towards your final examination mark, unless the Department grants an extension of time on the grounds that there are mitigating circumstances. Any application for such an extension should be made by your college Tutor or Director of Studies to the Director of Undergraduate Teaching, c/o Teaching Office, Cavendish Laboratory, ([email protected]). In such circumstances, you should submit the work as soon as possible after the deadline.

8 Part IA Physics 3.7 LECTURE LIST

PART IA PHYSICS

Departmental Contact: Helen Marshall, email: [email protected] Course Website: http://www.phy.cam.ac.uk/teaching/

All lectures are on M. W. F. at 9 All lectures take place in the Bristol-Myers Squibb Lecture Theatre, Chemical Laboratory, Lensfield Road.

For the up-to-date lecture list please go to: http://www.phy.cam.ac.uk/teaching/lectures.php

Laboratory Work takes place at the Cavendish Laboratory (West Cambridge). The experimental laboratories are open M. 2-5.45, Tu. 2-5.45, Th. 2-5.45 and F. 2-5.45. Students will be allocated a session within these times. All students must attend an introductory talk and register for Laboratory Work at 11.00 a.m. on W. 9 Oct. at the Cavendish Laboratory. The Laboratory may be approached by the Madingley Road, or via the Coton cycle and footpath. For cyclists and pedestrians the latter is strongly recommended. Laboratory work is continuously assessed.

Part IA Physics 9 PRINCIPLES OF CLASSICAL PHYSICS, QUANTUM PHYSICS & RELATIVITY

J M Riley, G A C Jones, A M Donald, S F Gull and M C Payne

This lecture course consists of five 12-lecture modules. It covers a number of fundamental topics in classical physics – mechanics, oscillations, waves and gravitational and electromagnetic fields – but also introduces some of the unusual non-classical ideas encapsulated in quantum physics and special relativity. In addition a number of concepts in the collection and analysis of experimental data – which form the basis for our understanding of the physical world – are also discussed.

Key ideas on the setting up of mathematical models to describe physical systems are introduced using mathematical tools such as differentiation, integration, complex numbers and vectors. The lectures will also introduce you to a variety of techniques for tackling physics problems which will be developed through illustrative examples.

Each module is accompanied by a set of examples, which tie in closely with the ideas and concepts introduced in the lectures; during the term you are expected to work through all these examples – averaging about six per week – with the help of your supervisor.

1 – DYNAMICS – J M Riley

Introduction to university physics: role of experiment; mathematical models; dimensional analysis; tackling physics problems.

Experimental physics: random and systematic errors; Gaussian probability distribution; mean, standard deviation, error in the mean; errors in functions of a single variable, combining errors in two variables; examples of techniques for dealing with systematic errors; graphs.

Dynamics: Concept of a force: tendency to produce motion; forces as vectors; action and reaction; friction. Calculus in physics: use of integration. Work: potential energy; stable and unsta- ble equilibrium. Kinematics: displacement, speed, velocity, acceleration. Newton’s laws of motion: equations of motion. Kinetic energy: concept and definition; principle of the conservation of energy. Linear momentum: concept and definition; conservation of linear momentum; rockets; elastic and inelastic collisions; impulse of a force. Frames of reference: relative velocities, inertial frames of reference, zero-momentum frame, collisions.

10 Part IA Physics 2 – OSCILLATING SYSTEMS – G A C Jones

Simple harmonic motion (SHM): equation of un-damped oscillation for a mass on a spring, its solution, relative phases of displacement, velocity and force. Approximations of oscillating systems to SHM: simple pendulum. Energy in SHM: vibration of two masses joined by a spring, quantum well.

Phasor diagrams: superposition of oscillations, beats, amplitude modulation.

SHM using complex numbers: Curves of time-dependence for an oscillator, amplitude, frequency, angular frequency and phase.

Damped oscillations: amplitude and energy decay, quality factor.

Forced oscillations: qualitative frequency response and resonance.

Revision of electrical circuits: voltage, current and charge in circuits, electrical resistance, Kirchhoff's laws, resistors in series and parallel. Inductors and capacitors. Circuits with exponen- tial decays: discharge of a capacitor through a resistor, decay of current through an inductor.

Oscillations in electrical circuits and complex impedance: Oscillation in an LC circuit, relative phases of voltages, charge and currents. Complex current and voltage in resistors, capacitors and inductors. Complex impedance. Electrical resonance in an LCR circuit, simple filter, bandwidth, Q factor. Relationship of behaviours seen in electrical systems to those of mechanical systems. Mechanical impedance.

3 – WAVES AND QUANTUM WAVES – A M Donald

Waves: The 1-D equation, application to waves on a string, sinusoidal solutions, amplitude, frequency wavelength, energy transport, transverse and longitudinal waves; boundary conditions at free or fixed end; superposition, interference; travelling and standing waves including complex form; plane waves in 2-D and 3-D, the wave vector and wave number.

Optics: Huygens’ Principle, laws of reflection and refraction, lenses, lens formulae, real and virtual images, the simple telescope and microscope.

Diffraction: diffraction using complex amplitudes, Young’s slits and the diffraction grating, finite slit using complex amplitude and via integration.

Quantum waves: reminder of wave-particle duality and de Broglie relation; introduction to the wavefunction and 1-D time independent Schrodinger equation; waves in wells and boxes and quantisation of wavelength; reflection at potential steps; penetration through a barrier and evanescent waves.

Part IA Physics 11 4 – ROTATIONAL MECHANICS AND SPECIAL RELATIVITY – S F Gull

Rotational Mechanics: Turning moments: lever balance; turning moment as a vector; moment of a couple; conditions for static equilibrium. Centre of mass: calculation for a solid body by integration. Circular motion: angle, angular speed, angular acceleration; as vectors; rotating frames; centripetal force. Angular momentum: concept and definition; angular impulse; conservation. Moment of inertia: calculation of moment of inertia; theorems of parallel and perpendicu- lar axes. Rotational kinetic energy: simple collisions involving angular rotation. Gyroscope: how it works; precession.

Special Relativity: Historical development: problems with classical ideas; the Aether; Michel- son-Morley experiment. Inertial frames: Galilean transformation. Einstein’s postulates: statement; events, and intervals between them; consequences for time intervals and lengths; Lorentz transformation of intervals; simultaneity; proper time; twin paradox; causality; world lines and space–time diagrams. Velocities: addition; aberration of light; Doppler effect. Relativistic mechanics: momentum and energy; definitions; what is conserved; energy–momentum invariant. Nuclear binding energies, fission and fusion.

5 – GRAVITATIONAL AND ELECTROMAGNETIC FIELDS – M C Payne

Gravitation: Newton’s law, measurement of G. Action at a distance and concept of a local force field. Properties of conservative fields, including potential energy as a path integral. Superposition of fields. Gauss’ law for gravity with simple quantitative applications.

Orbits: Kepler’s laws. Derivation of elliptical orbits for planetary motion from Newton’s law. Simple orbital calculations. Qualitative examples of gravity at work including tidal effects.

Electrostatic Fields: Static electricity, Coulomb’s Law for point charges, the electric field E and the corresponding potential for point charges and electric dipoles. Gauss’ law for electrostatic fields. Properties of ideal conductors. Capacitance including calculation for simple geometries. Mention effects of dielectric materials on capacitance and dipole moment of water molecule.

Magnetic Fields: Properties of bar magnets. Magnetic flux density B. Magnetic dipoles and currents as sources of B. Lorentz force and motion of charged particles in electric and magnetic fields; J.J. Thomson’s experiment. Ampère and Biot-Savart laws, calculation of B field in simple cases. Faraday’s law of induction; self and mutual inductance, energy stored in B field.

Maxwell’s Equations: Displacement current term. Integral and differential statements. Exam- ple of plane wave solutions.

BOOKS

There are two books recommended for the IA Physics course – these will be available in College libraries. Lecturers will give references both to relevant sections of these books, and to worked examples in them, which help explain or expand on the material they present in their lectures. Similarly, the question sheets may sometimes refer to the examples in these books for students who wish to try additional problems. This is to encourage you to develop your skills in utilising the more extensive resource material provided in text-books to deepen your understanding of physics.

Understanding Physics (Second Edition), Mansfield M & O’Sullivan C (Wiley 2011) Physics for Scientists and Engineers (Extended Version), Tipler P A & Mosca G (6th Edition, Freeman 2008)

12 Part IA Physics IA PRACTICAL CLASS

J M Riley and D A Green

The aim of the Part IA practical course is to teach basic experimental, data-analysis and record- keeping skills. The experiments have been chosen to develop particular skills, although the experiments in the Lent and Easter terms also reinforce material from the lectures. Students work in pairs throughout.

Michaelmas Term

Four experiments are carried out. These are primarily intended to teach experimental skills – including how to keep a good laboratory notebook – and to introduce experimental errors and their treatment. The required theory, as well as a general overview of experimental skills, will be included in the “Dynamics” lecture course. Marks for the first practical (E1) do not count towards the final total. E1. Attenuation of -ray photons. Through the statistics of radioactive decay, this aims to develop an understanding of random and systematic errors in count rates and to estimate the linear attenuation coefficient for photons in lead.

E2. Galileo’s rolling ball experiment. This aims to introduce the basic methods of experimental measurement and errors through an investigation of the acceleration of a mass rolling down a ramp.

E3. Thermal excitation in a semiconductor. This experiment measures the variation of the electrical resistance of a semiconductor with temperature, testing the behaviour predicted by quantum physics.

E4. Measurement of g using a rigid pendulum. The aim of this experiment is to measure the value of g with a precision of about one part in a thousand using the oscillations of a rigid pendulum.

Lent Term

Four experiments are carried out, all of which illustrate material from the lecture courses. E5, E6 and E7 use concepts introduced in the “Oscillating systems” course. E5 is an investigation of damped oscillations and resonance in a mechanical system. E6 is an introduction to measuring electrical signals with a picoscope; the picoscope is then used in E7 to investigate electrical resonance. E8 investigates the geometric optical properties of simple lenses and mirrors, illustrating material from the section on optics in the “Waves and quantum waves” course. E5. Mechanical resonance*. This experiment studies the free and forced rotational oscillations of a torsion pendulum, and investigates the phenomenon of resonance and the effect different levels of damping have on the motion.

E6. Electrical measurement. This experiment introduces the picoscope as a measuring instrument, through experiments looking at the output of a signal generator.

E7. Electrical resonance and signal filtering*. In this experiment the picoscope is used to study free and forced oscillations in LCR resonant circuits, and a practical application of an LCR network is investigated.

Part IA Physics 13 E8. Geometric optics using lenses and mirrors*. This practical involves a series of simple experiments demonstrating the properties of optical lenses and mirrors, and real and virtual images.

Easter Term

Two experiments are carried out, illustrating material from the lecture course “Waves and quantum waves”. E9 is an investigation into diffraction by slits and gratings. E10 looks at the photoelectric effect – one of the experiments fundamental to the development of quantum physics. Half the class will carry out Experiment E9 in the first session of the Easter term, followed by E10 in the second session; the other half of the class will do E10 in the first session and E9 in the second. E9. Diffraction of laser light by slits and gratings. This is a quantitative investigation into the diffraction patterns produced by double and multiple slits when illuminated by a laser.

E10. The photoelectric effect. This practical investigates the photoelectric effect; an estimate of Planck’s constant is obtained, using the dependence of stopping voltage on the frequency of the incident light.

Formal Reports

Students are required to produce two formal reports which are assessed by a Head of Class; the marks awarded count towards the end-of-year assessment. The first report, to be handed in at the start of the Lent term, will be based on one of the experiments carried out in the Michaelmas term. The second one, to be handed in at the start of the Easter term, will be a full report on one of the three starred* Lent-term experiments (i.e. E5, E7 or E8).

BOOKS

Practical Physics, Squires G L (4th edn CUP 2001). Experimental methods: An Introduction to the Analysis and Presentation of Data, Kirkup L (Wiley 1994). Experimental Physics: Modern Methods, Dunlap R A (OUP 1989) An Introduction to Experimental Physics, Cooke C (Routledge 1996) Measurements and their Uncertainties: A Practical Guide to Modern Error Analysis, Hughes I G & Hase T P A (Oxford 2010)

14 Part IA Physics Part IB Physics A

Comments may be sent to [email protected] Enquiries/queries: [email protected]

4.1 INTRODUCTION AND COURSE same time on weekdays during Michaelmas Term. This course is supervised, and covers all the addi- AIMS tional mathematics required for both Part IB The objective of the IB Physics A course is to pro- Physics courses, and for the Part II Physics core vide a self-contained package of quantum and and options courses. It does not provide full cov- condensed matter physics. The course builds on erage of the mathematics assumed for the Part II IA Physics and offers a firm grounding in impor- Theoretical Physics (TP) courses, but mathemati- tant areas of physics that are very useful for scien- cally-able students would need to do some extra tists with a wide range of career destinations. It work during the long vacation after Part IB in or- can be taken by those not taking Physics B; in this der to catch up. case IB Physics A might, for able students, lead to Half Subject Physics in Part II Physical Sciences 4.3 THE EXAMINATION but does not by itself lead to Part II Physics. The IB Physics A examination consists of two While it is also possible to take IB Physics B with- three-hour papers. Details of the material covered out IB Physics A, for the majority of students in each paper will be published in a Form and wishing to take a single physics option in Part IB, Conduct Notice during the course of the year. Physics A is likely to be the more attractive option. Note that the NST IB courses were changed considerably in 2007-08, with the previous Students will be contacted by e-mail and asked to ‘Physics’ and ‘Advanced Physics’ material register on-line at www.phy.cam.ac.uk/teaching re-arranged into ‘Physics A’ and ‘Physics before the start of Michaelmas Term. Those tak- B’. ing only one of Physics A or Physics B must register for practical classes between 2.00 Specific information about the examination is pm and 4.00 pm on Tuesday 8th October given in notices put up on the Part IB examination 2013 at the Cavendish Laboratory. Stu- notice board outside the Part IB laboratory. The dents taking both Physics A and Physics B practicals are continuously assessed and overall should register at 2.00pm on Wednesday count approximately 25% towards the IB Physics 9th October 2013 at the Cavendish Labora- A examination, with about 40% of this coming tory. from a formal report on one of the experiments (for those not doing Physics B) or from a group 4.2 THE CONTENT OF THE presentation of an extended investigation (for COURSE those doing both Physics A and Physics B); full details are given in the class manual and additional The lecture course Oscillations, Waves and Optics help is given in the booklet Keeping Laboratory covers central aspects of physical phenomena that Notes and Writing Formal Reports. underpin much of physics. The Quantum Physics course builds on this and treats quantum phenomena both from the wave equation and by means of operator methods. Condensed Matter Physics shows how ideas from waves and quantum mechanics can be applied to understand the properties of solids. The practical class and Ex- perimental Methods lectures are integrated together to provide training on designing and doing experiments and on analysing the results. Physics A and Physics B both require mathematics beyond that in the syllabus for IA Mathematics for Natural Sciences; students not taking the NST Part IB subject Mathematics should attend the lectures on Mathematical Methods given at the

Part IB Physics A 15 4.4 SOME IMPORTANT DATES Note: This list is not exhaustive, and may be superseded by announcements on the TIS

Tuesday 8th October 2013 Start of Michaelmas full term. Tuesday 8th October 2013 14.00-16.00 Practical Registration for Students taking IB Phys- ics A or B at the Cavendish Laboratory Wednesday 9th October 2013 14.00 Practical registration for Students taking IB Phys- ics A and B at the Cavendish Laboratory Friday 6th December 2013 End of Michaelmas full term Monday 9th December 2013 16.00 Head-of-Class report must have been handed in to the IB Practical Class if chosen for submission (see synopsis of Physics A practical class for details) Tuesday 14th January 2014 Start of Lent full term Friday 14th March 2014 End of Lent full term Monday 17th March 2014 16.00 Head-of-Class report must have been handed in to the IB Practical Class if chosen for submission (see synopsis of Physics A practical class for details) Tuesday 22nd April 2014 Start of Easter full term Tuesday 22nd April 2014 16.00 Extended Investigation presentation slides (only for students take Physics A and Phys- ics B) must have been submitted to relevant Head of Class Friday 13th June 2014 End of Easter full term

Late Submission of Work In accordance with the University’s regulations, work submitted after the advertised deadline will not count towards your final examination mark, unless the Department grants an extension of time on the grounds that there are mitigating circumstances. Any application for such an extension should be made by your college Tutor or Director of Studies to the Director of Under- graduate Teaching, c/o Teaching Office, Cavendish Laboratory, (teaching- [email protected]). In such circumstances, you should submit the work as soon as possible after the deadline.

16 Part IB Physics A 4.5 LECTURE LIST NATURAL SCIENCES TRIPOS

PART IB PHYSICS A

Departmental Contact: Helen Marshall, email: [email protected] Course Website: http://www.phy.cam.ac.uk/teaching/

Lectures are given in the Cockcroft Lecture Theatre, New Museums Site, M. W. F. 12 unless otherwise stated.

For the up- to-date lecture list please go to: http://www.phy.cam.ac.uk/teaching/lectures.php

Laboratory Work takes place at the Cavendish Laboratory (West Cambridge). The experimental laboratories are open M. 2-5.45, Tu. 10-5.45, Th. 10-5.45 and F. 2-5.45. Students will be allocated periods within these times. Students taking both Part IB Physics A and Part IB Physics B should register at 2.00 p.m. on W. 9 Oct. at the Cavendish Laboratory. Students taking Part IB Physics A or IB Physics B, must register between 2.00 p.m. and 4.00 p.m. on Tu. 8 Oct., when they will be allocated practical sessions that fit with their other IB subjects. Laboratory work is continuously assessed.

Part IB Physics A 17 EXPERIMENTAL METHODS

C G Smith

Physics is an empirical subject based on measuring physical phenomena. This course introduces techniques for putting together experiments and analysing the results. Many complex systems, ranging from telescopes to mobile phones, can often be understood in terms of a set of black boxes with simple interactions between them. This systems approach is particularly useful in experimental physics where the signal chain from the physical phenomenon under investigation to a measurement can involve many sequential and complex components such as transducers, amplifiers, filters and detectors.

The first part of this course explores this process – with reference to some of the experiments undertaken in the practical classes – while the second part introduces you to some of the essential material that a physicist needs to know so as to design experiments (including computational ones), to analyse data, and to evaluate other people’s results.

This course requires the material covered in the IA Physics and Maths for Natural Scientists courses, and exploits the ideas of Fourier theory that are more fully developed in the Mathematics options that run in parallel with this course in the Michaelmas term. Ideas of Fourier decomposition will be introduced, along with Fourier series, but they are covered more fully in the Mathe- matics option.

Systems: Impedance and measurement. Operational amplifiers and filters. Positive and negative feedback with ideal and non-ideal amplifiers.

Random errors: examples, propagation, reduction with repeated sampling.

Systematic errors: examples, designs to reduce them (e.g. nulling), selection effects.

Basic data handling: taking and recording data. The right plot; error bars. Sampling, aliasing, Nyquist’s criterion. Digitization errors.

Exclusion of unwanted influences: filtering, phase-sensitive detection and lock-in amplifiers. Vibrational, thermal and electrical shielding.

Probability distributions: binomial, Poisson and Gaussian; central limit theorem; shot noise and Johnson noise.

Parameter estimation: likelihood, inference and Bayes’ theorem, chi-squared, least-squares, hypothesis testing, non-parametric tests.

Getting the message across: writing a scientific report and presenting results.

BOOKS

There are no books which cover the complete course syllabus, and so each lecture handout will be augmented with a set of supplementary notes. Reading these prior to the lectures will be helpful. The following books may be useful to refer to on certain aspects of the course:

The Art of Electronics, Horowitz P & Hill W (2nd edn CUP 1989) Analogue and Digital Electronics for Engineers, Ahmed H & Spreadbury P J (CUP 1984) An Introduction to Experimental Physics, Cooke C (CRC Press 1996) Practical Physics, Squires G L (4th edn CUP 2001) Experimental Physics: Modern Methods, Dunlap R A (OUP 1988)

Copies of some of these will be available for consultation in the practical classes.

18 Part IB Physics A

OSCILLATIONS, WAVES AND OPTICS

J S Richer

An understanding of waves is fundamental to many areas of physics. This course develops further the ideas presented in the Part IA courses on oscillations and waves, and introduces the theory of diffraction. First, the physics and mathematics of oscillations and waves are revised, and applied to a variety of physical systems. The use of the Fourier Transform as a powerful tool for understanding the behaviour of general linear systems is then introduced, and used to relate the time- domain and frequency-domain behaviour of damped electrical and mechanical oscillators. Fi- nally, these ideas are further developed in the context of classical optics, with particular regard to diffraction and interference phenomena.

Oscillations: Driven damped oscillations, frequency response, bandwidth, Q-factor. Impulse response and transient response.

Waves: Revision of 1-d wave equation. Waves on a stretched string. Polarisation. Wave impedance. Reflection and transmission. Impedance matching. Compression waves in a fluid. Waves in 2 and 3 dimensions. Standing waves in a box. Wave groups, group velocity, dispersion. Waveguides: cut-off and dispersion.

Fourier transforms in linear systems: Linear response and superposition in physics. Fou- rier series and Fourier transforms. Frequency response as Fourier transform of pulse response. Convolution. Applications to oscillating systems.

Optics and diffraction: Huygen’s principle as a solution to the wave equation. Fraunhofer diffraction, Fraunhofer integral, relation to Fourier transform. Wide slit as example of extended source. The width of spectral lines. Gratings and spectroscopy. 2-d apertures, circular apertures, Babinet’s principle. Fresnel diffraction, Cornu spiral, zone plate.

Interference: Thin film interference. Fabry-Perot etalon. Michelson interferometer, Fourier transform spectroscopy.

BOOKS

Vibrations and Waves in Physics, Main I G (3rd edn CUP 1993) The Physics of Vibrations and Waves, Pain H J (5th edn Wiley 1999) Vibrations and Waves, French A P (Chapman & Hall 1971) Optics, Hecht E (4th edn Addison-Wesley 2001)

Part IB Physics A 19 QUANTUM PHYSICS

V Gibson

The Birth of Quantum Physics: Quantization of electromagnetic radiation: u-v catastrophe, photoelectric effect, Compton scattering. Wave properties of matter: de Broglie hypothesis, the Bohr model of the atom and atomic structure, electron and molecular diffraction. The central role of Planck’s constant.

Wave Particle Duality and the Uncertainty Principle: Young’s double-slit experiment. Free particle in one dimension: plane waves and wave-packets. The Heisenberg Uncertainty Prin- ciple. Time evolution of wave-packets: dispersion and propagation.

The Schrödinger Equation: Time-independent and time-dependent Schrödinger Equation.

Wave Mechanics of Unbound Particles: Particle flux. One dimensional potentials and boundary conditions. The potential step: reflection and transmission. The potential barrier: tunnelling. Radioactivity : and decay.

Wave Mechanics of Bound Particles: The infinite square well potential and bound states. Normalization, parity and orthogonality. The Correspondence principle. The finite square well potential. The harmonic oscillator: vibrational specific heat. Wave mechanics in 3D: particle in a box, degeneracy and 3D harmonic oscillator.

Operator Methods: Operators, observables, linear hermitian operators and operator algebra. Dirac notation: eigenstates and eigenvalues. Orthogonality, degeneracy and completeness of eigenstates. Compatible and incompatible observables: commuting operators and simultaneous eigenstates, non-commuting operators, generalized uncertainty relations, minimum-uncertainty states. Ladder operators: the harmonic oscillator, equipartition.

Time-Dependent Quantum Mechanics: Time-dependence: expectation values, Ehrenfest’s theorem, stationary states, the time-evolution operator, time-energy uncertainty relation, conserved quantities.

Quantum Mechanics in Three Dimensions: General formulation. Orbital angular momentum: eigenfunctions and parity. The 3D harmonic oscillator. The rigid rotator: rotational specific heats of gases. Central potentials: conservation of angular momentum, quantum numbers, separation of variables. The hydrogen atom. Non-central potentials and hybridization.

Spin: The Stern-Gerlach experiment. Spin angular momentum, spin operators, spin eigenstates. Combining spin and orbital angular momentum, combining spins. Matrix methods. Pauli spin matrix and spinors.

Identical Particles: Identical particle symmetry: multiparticle states, fermions and bosons, exchange operator, exclusion principle, symmetry and interacting particles, counting states. Two- electron system: helium ground and excited states. The Standard Model of Particle Physics.

20 Part IB Physics A BOOKS

Books to consider buying: Quantum Physics, Gasiorowicz S (Wiley 2003) A fine exposition of the subject, suitable for Part IB and Part II. Quantum Mechanics, McMurry S M (Addison-Wesley 1994). Quite well suited to the course and includes a disc with interactive illustrative programs. Quantum Mechanics, Rae A I M (Hilger 1992) A good alternative to Gasiorowicz or McMurry, much shorter and consequently less full in its treatment of difficult points. Quantum Mechanics Mandl F (Wiley 1992). A good book, suitable for Part IB and Part II. Introduction to Quantum Mechanics, Bransden and Joachin (Longman, 1989). A thick book, with very full coverage but perhaps less elegance and clarity than Gasiorowicz. Problems in Quantum Mechanics, Squires (CUP, 1995). Worked solutions and summaries, ex- tending beyond this course.

Books for College libraries: Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, Eisberg R and Resnick R (Wiley 1985). Too elementary to recommend as a main textbook, but very good descriptive coverage of a wide range of quantum phenomena.

Part IB Physics A 21 CONDENSED MATTER PHYSICS

J Ellis

Periodic Systems: Overview of crystal structures, the reciprocal lattice.

Phonons: Phonons as normal modes – classical and quantum picture. 1D monatomic chain, 1D diatomic chain, examples of phonons in 3D. Debye theory of heat capacity, thermal conductivity of insulators.

Electrons in solids: Free electron model: Fermi-Dirac statistics, concept of Fermi level, electronic contribution to heat capacity. Bulk modulus of a nearly free electron metal. Electrical and thermal conductivity. Wiedemann-Franz law. Hall effect.

Nearly free electron model: Derivation of band structure by considering effect of periodic lattice on 1-D free electron model. Bloch’s theorem. Concept of effective mass. The difference between conductors, semiconductors and insulators explained by considering the band gap in 2D. Hole and electron conduction.

Doping of semiconductors, p and n types, pn junctions – diodes, LEDs and solar cells.

BOOKS

In general the course follows the treatment in Solid State Physics, J.R. Hook and H.E. Hall (2nd edition, Wiley, 1991).

Introduction to Solid State Physics, Charles Kittel (8th edition, Wiley, 2005) is highly recommended. (need not be the latest edition)

Other books, generally available in College libraries and may usefully be consulted:

The Solid State, Rosenberg H M (3rd edn OUP 1988) Solid State Physics, Ashcroft N W and Mermin N D (Holt-Saunders 1976).

22 Part IB Physics A MATHEMATICAL METHODS

C A Haniff

This course is offered to students taking either or both of Physics A and Physics B, but who are not taking "Mathematics'' in NST IB. In conjunction with the material from "Mathematics'' in NST IA, this course provides the mathematics required for Physics A and Physics B in NST IB, and the core and option lecture courses in Part II Physics.

This course requires the material covered in the NST IA Mathematics and Physics for Natural Sci- entists courses, and uses examples showing how the mathematical methods introduced can be utilised in a wide range of physical problems. Fluency with integration of the tools from NST IA Mathematics with the topics taught in NST IA Physics is required.

Vector and Scalar fields in Cartesian coordinates: Basic definitions of scalar and vector fields. Line, surface, and volume integrals. Grad, Div and Curl.  and Laplacian operators. Diver- gence Theorem, Stokes' Theorem, and Green's Theorem. Conservative fields. Maxwell's equations as example of vector differential operators.

Cylindrical, Spherical, and Curvilinear coordinate systems: Basic definitions of cylindrical and spherical coordinate systems. Application to scalar and vector fields. Curvilinear coordinate systems. Vector differential operators in cylindrical, spherical, and curvilinear coordinate systems.

Variational Principles: Lagrange multipliers. Euler–Lagrange equation.

Fourier Series: Fourier series of periodic functions using trigonometric functions. Discontinui- ties and Gibbs phenomenon. Even and odd functions. Fourier series in complex form. Solving one-dimensional differential equations using Fourier series. Notions of completeness and orthogonality.

Fourier Transforms: Definition. Symmetry considerations. Fourier transforms of differentials. The Dirac delta function. Convolution. Green's functions. Parseval's theorem.

Differential Equations: Laplace’s equation, Poisson's equation, the diffusion equation, the wave equation, Helmholtz equation, Schrödinger's equation. Separation of variables in Cartesian, cylindrical polar, and spherical polar coordinate systems. Summary of common differential equations and orthogonal functions. Examples, including Bessel, Legendre, Hermite functions etc. Analogy between function expansions and geometrical vector expansions: orthogonality and completeness. Convergence of power series. Power series expansions and solution of ordinary differential equations. Legendre polynomials, Bessel functions, Hermite polynomials and Spherical Harmonics illustrated by examples. Brief summary of Sturm–Liouville theory.

Matrices and Tensors: Basic matrix algebra. Determinants. Special matrix types, including Hermitian matrices. Eigenvalues, eigenvectors and diagonalization. Basic concept of a tensor. Summation convention: Kronecker delta and Levi–Civita symbol.

BOOKS

Mathematical Methods in the Physical Sciences, Boas M L (3rd edn, Wiley 2006) Mathematical Methods for Physics and Engineering, Riley K F, Hobson M P and Bence S J (3rd edn, CUP 2006)

Part IB Physics A 23 GREAT EXPERIMENTS

A N Lasenby and others

This non-examinable course looks at a selection of great experiments, considering both the special techniques, and also the context in which they were conceived and their effect on our understanding of physics. Each lecture will cover a different experiment and these are likely to include the following:

Tests of classical gravity: Eotvos experiment, Precision measurements of G, search for higher dimensions at the mm-scale.

Understanding neutrinos: Chemical methods (the Homestake mine experiment), the Solar neutrino problem, neutrino oscillations at SNO.

The search for the Higgs boson.

The Cosmic Microwave Background: Discovery (Penzias and Wilson), implications for Big Bang cosmology, fluctuations (COBE) and the Planck Satellite Experiment.

The Structure of DNA: The story of Crick and Watson’s determination of the structure of DNA is well known; this account will include some of the Physics involved in both 1952 and the present day.

Ultracold atoms: The need for a low-temperature gas, laser cooling, Bose-Einstein condensation, atom scattering from “optical crystals”.

Fundamental tests of Quantum Mechanics: “Spooky action at a distance”. Hidden variables and Bell’s inequality, demonstrations of Quantum entanglement.

The search for Extrasolar Planets.

24 Part IB Physics A IB PRACTICAL CLASS – PHYSICS A

W Allison and R T Phillips

The Practical Classes for the IB Physics options (i.e. both the A & B courses) are organized around a set of fourteen experiments, six in the Michaelmas term and eight in the Lent term. Students taking the A, B or both A+B courses undertake different numbers and combinations of these experiments during the year. Candidates taking only the Physics A course will usually undertake a total of 7 experiments during the year (3 in the Michaelmas term and 4 in the Lent term) attending two 3¾ hour long afternoon sessions (over a fortnight) per experiment. Candidates taking both the Physics A and Physics B courses are expected to undertake 6 experiments in the Michaelmas term and 4 experiments in the Lent term, but will complete each of these over the course of a week (usually in one day). They also undertake a longer experimental investigation in groups of four, spread over the final two weeks of the Lent term.

For full details of the classes, see p.38

Part IB Physics A 25 Part IB Physics B

Comments may be sent to [email protected] Enquiries/queries: [email protected]

introduces key concepts in fluid mechanics. Thermodynamics provides an introduction to 5.1 INTRODUCTION AND COURSE classical thermodynamics and kinetic theory. A AIMS non-examinable course “Great Experiments” provides valuable insight into the importance of ex- The IB Physics B covers a range of topics that are periments in the progress of physics, and their complementary to the IB Physics A course. Stu- historical context. The Computing course pro- dents wishing to proceed to part II Physics must vides an introduction to C++ programming tech- take both Physics A and Physics B. niques and their application in physics-based Students taking both courses combine them with problems. The practical class extends the teach- one other IB subject. While NST IB Mathematics, ing of experimental physics and analysis offered is frequently taken, and is useful for those wishing in IB Physics A. to pursue Theoretical Physics options within the Physics A and Physics B both require mathemat- Part II Physics course, students should be advised ics beyond that in the syllabus for IA Mathematics that this is both a demanding and constraining for Natural Sciences; students not taking the NST choice. (For students taking subjects other than Part IB subject Mathematics should attend the Mathematics, appropriate support is provided lectures on Mathematical Methods given at the through the Michaelmas Term course in Mathe- same time on weekdays during Michaelmas Term. matical Methods.) The selection of a different This course is supervised, and covers all the addi- subject in place of NST IB Mathematics provides tional mathematics required for both Part IB greater breadth and gives greater choice of Part Physics courses, and for the Part II Physics core II/III subjects within the Natural Sciences Tripos, and options courses. It does not provide full cov- should Part IB physics not prove to be rewarding. erage of the mathematics assumed for the Part II It is possible to take IB Physics B without IB Phys- Theoretical Physics (TP) courses, but mathemati- ics A, but this is not adequate preparation for Part cally-able students would need to do some extra II Physics. The practical work draws heavily work during the long vacation after Part IB in or- on material from Physics A in the der to catch up. Michaelmas Term, and students taking just Physics B are advised to attend at least the 5.3 THE EXAMINATION Experimental Methods lectures from Phys- The IB Physics B examination consists of two ics A for necessary background. For the ma- three-hour papers. Specific information about the jority of students wishing to take a single physics examination is given in notices put up on the Part option in Part IB, Physics A is likely to be the IB examination notice board outside the Part IB more attractive option. laboratory. The practical elements of this course Students will be e-mailed and asked to register via (i.e. the practicals and computing) are continu- http://www.phy.cam.ac.uk/teaching/ before the ously assessed and overall count approximately start of Michaelmas Term. 25% towards the IB Physics B marks. (Students should note that roughly 40% of the marks for the Students not taking both Physics A and practicals will come from a Head of Class Re- Physics B must register between 2.00 pm port/Group Presentation). Full details are in the and 4.00 pm on Tuesday 8th October 2013. class manual and additional help is given in the Students taking both Part IB Physics A and booklet Keeping Laboratory Notes and Writing Part IB Physics B should register at 2.00 Formal Reports. pm on Wednesday 9th October 2013 at the Cavendish Laboratory.

5.2 COURSE CONTENT The lectures on Electromagnetism cover key concepts in this important subject. Classical Dynam- ics provides more advanced approaches to classical problems than were given in Part IA, and 26 Part IB Physics B 5.4 SOME IMPORTANT DATES Note: This list is not exhaustive, and may be superseded by announcements on the TIS

Tuesday 8th October 2013 Start of Michaelmas full term Tuesday 8th October 2013 14.00–16.00 Practical registration for Students taking IB Physics A or B at the Cavendish Laboratory Wednesday 9th October 2013 14.00 Practical registration for Students taking IB Physics A and Physics B at the Cavendish Laboratory Friday 6th December 2013 End of Michaelmas full term Monday 9th December 2013 16.00 Head-of-Class report must have been handed in to the IB Practical Class if chosen for submission (see synopsis of Physics B practical class for details) Tuesday 14th January 2014 Start of Lent full term Friday 14th March 2014 End of Lent full term Monday 17thMarch 2014 16.00 Head-of-Class report must have been handed in to the IB Practical Class if chosen for submission (see synopsis of Physics B practical class for details) Tuesday 22nd April 2014 Start of Easter full term Tuesday 22nd April 2014 16.00 Extended Investigation presentation slides (only for students take Physics A and Physics B) must have been submitted to relevant Head of Class Friday 6th June 2014 Deadline for obtaining approval for Part IB students to do Long-Vacation Work for submission as part of Part II Friday 13th June 2014 End of Easter full term

Late Submission of Work In accordance with the University’s regulations, work submitted after the advertised deadline will not count towards your final examination mark, unless the Department grants an extension of time on the grounds that there are mitigating circumstances. Any application for such an extension should be made by your college Tutor or Director of Studies to the Director of Under- graduate Teaching, c/o Teaching Office, Cavendish Laboratory, (teaching- [email protected]). In such circumstances, you should submit the work as soon as possible after the deadline.

Part IB Physics B 27

5.5 LECTURE LIST NATURAL SCIENCES TRIPOS

PART IB PHYSICS B

Departmental Contact: Helen Marshall, email: [email protected] Course Website: http://www.phy.cam.ac.uk/teaching/

Lectures are given in the Cockcroft Lecture Theatre, New Museums Site, M.W.F. 9 unless otherwise stated.

For the up-to-date lecture list please go to: http://www.phy.cam.ac.uk/teaching/lectures.php

Laboratory Work takes place at the Cavendish Laboratory (West Cambridge). The experimental laboratories are open M. 2-5.45, Tu. 10-5.45, Th. 10-5.45 and F. 2-5.45. Students will be allocated periods within these times. Students taking both Part IB Physics A and Part IB Physics B should register at 2.00 p.m. on W. 9 Oct. at the Cavendish Laboratory. Students taking Part IB Physics B or IB Physics A, must register between 2.00 p.m. and 4.00 p.m. on Tu. 8 Oct., when they will be allocated practical sessions that fit with their other IB subjects. Laboratory work is continuously assessed.

28 Part IB Physics B ELECTROMAGNETISM

S Withington

The electromagnetism course further develops the idea of electric and magnetic fields introduced in Part IA, with electrostatics and magnetostatics being treated as special cases of Maxwell’s equations. The course introduces dielectric and magnetic media, and examines wave propagation in free space, as well as in insulating and conducting media and on transmission lines and waveguides

Introduction: Electromagnetism in physics, and the role of Maxwell’s equations.

Electrostatic fields: Electrostatic force, electric field, potential, grad, curl, line integrals, Stokes’s theorem, conservative fields, electric monopoles, electric dipoles, field of a dipole, couple and force on a dipole, energy of a dipole, multipole expansions, electric flux, divergence, divergence theorem, Gauss’s law, solutions for simple geometries, Laplace’s and Poisson’s equations, boundary conditions and uniqueness, conducting sphere in uniform E field, method of images, point charge near conducting sphere, line charge near conducting cylinder, capacitance, capacitance of parallel cylinders, energy stored in electric field, force and virtual work, force on charged conductor.

Electrostatic fields in dielectric materials: Isotropic dielectrics, polarisation, polarisation charge density, Gauss’s law for dielectric materials, permittivity and susceptibility, properties of D and E, boundary conditions at dielectric surfaces, field lines at boundaries, relationship between E and P, thin slab in field, dielectric sphere in field, energy density in dielectrics, general properties of dielectrics.

Magnetostatic fields: Force on and between current elements, magnetic flux, the ampère, .B=0, magnetic dipoles, force and couple on a dipole, energy, magnetic scalar potential, solid angle of a loop, Ampère’s law, magnetic vector potential.

Magnetostatic fields in magnetic materials: magnetisation, existence of diamagnetism and paramagnetism, permeability and magnetic susceptibility, properties of B and H, boundary conditions at surfaces, methods for calculating B and H, magnetisable sphere in uniform field, elec- tromagnets.

Time varying electromagnetic fields: Faraday’s law, emf, electromagnetic induction, Fara- day’s law for a circuit, interpretation of Faraday’s emf, self-inductance, inductance of long sole- noid, coaxial cylinders, parallel cylinders, mutual inductance, transformers, magnetic energy density.

Electromagnetic waves: equation of continuity, displacement current, Maxwell’s equations, electromagnetic waves, velocity of light, plane waves in isotropic media, energy density, Poynting’s theorem, radiation pressure and momentum, insulating materials, plasmas and the plasma frequency, evanescent waves. characteristic impedance, reflection and transmission at an angle, total internal reflection, conducting media, skin effect, guided waves, transmission lines, characteristic impedance; coaxial, parallel-wire, strip transmission lines; power flow; terminated lines, matching, reflection and transmission coefficients, impedance of short circuited lines, impedance matching, introduction to waveguides, TE and TM modes, waveguide equation, cut-off frequency, characteristic impedance, cavity resonators, optical fibres.

Summary of Maxwell’s equations: Restatement of equations, physical interpretation, classes of solutions, and applications.

Part IB Physics B 29 BOOKS

Electricity and Magnetism, Duffin W J (4th edn McGraw-Hill 1990). A general introductory text. Fields and Waves in Communication Electronics, Ramo S, Whinnery JR, and van Duzer T (2nd edn Wiley 1984). This text is aimed at engineers. It has an attractive style and achieves a good balance between mathematical rigour and physical insight. It provides an excellent introduction to the subject. Electromagnetism, Grant I S and Phillips W R (2nd edn Wiley 1990). This treatment is at about the right level for the course. It is easier to read than Bleaney & Bleaney, but does not go as far. Electricity and Magnetism, Bleaney B I and Bleaney B (3rd edn OUP 1989) (two volumes). A classic text that will see you through Part IB and Part II, but it is currently out of print.

30 Part IB Physics B CLASSICAL DYNAMICS

D A Green

This course builds on the ideas introduced in NST Part IA “Physics”, using the machinery of vector calculus taught in NST Part IA “Mathematics”. The main areas covered are orbits, rigid body dynamics, normal modes and continuum mechanics (elasticity and fluids).

Newtonian mechanics, frames of reference: Review of Part IA mechanics: many-particle system, internal and external forces and energy. Central forces, motion in a plane. Non-inertial frames, rotating frames, centrifugal and Coriolis forces. Examples.

Orbits: Effective potential and radial motion, bound and unbound orbits. Inverse-square law orbits, circular and elliptic, Kepler's laws. Escape velocity, transfer orbits, gravitational slingshot. Hyperbolic orbits, angle of scattering, repulsive force. Two-body problem, reduced mass. General features of three-body problem. Brief treatment of tidal effects in gravitational systems.

Rigid body dynamics: Instantaneous motion of a rigid body, angular velocity and angular momentum, moment of inertia tensor, principal axes and moments. Rotational energy, inertia el- lipsoid. Euler's equations, free precession of a symmetrical top, space and body frequencies. Forced precession, gyroscopes.

Introduction to Lagrangian mechanics: Generalised coordinates. Hamilton’s principle and Lagrange’s equations. Symmetries and conservation laws. Conservation of the Hamiltonian for time-independent systems.

Normal modes: Analysis of many-particle system in terms of normal modes. Degrees of freedom, matrix notation, zero-frequency and degenerate modes. Continuum limit, wave equation. Standing waves, energy and normal modes. Motion in three dimensions, modes of molecules.

Elasticity: Hooke's law, Young's modulus, Poisson's ratio. Bulk modulus, shear modulus, stress tensor, principal stresses. strain tensor. Elastic energy. Torsion of cylinder. Bending of beams, bending moment, boundary conditions. Euler strut. Brief treatment of elastic waves.

Fluid dynamics: Continuum fields, material derivatives, relation to particle paths and streamlines. Mass conservation, incompressibility. Convective derivative and equation of motion. Ber- noulli's theorem, applications. Velocity potential, applications: sources and sinks; flow past a sphere and cylinder; vortices; Magnus effect. Viscosity, Couette and Poiseuille flow. Reynolds number, lamina and turbulent flow.

BOOKS

Classical Mechanics, Barger V D and Olsson M G (McGaw-Hill, 1995). Fluid Dynamics for Physicists, Faber T E (Cambridge, 1995). Lectures on Physics, Feynman R P, Leighton R B and Sands S L (Addison Wesley 1964). Principles of Dynamics, Greenwood D T (Prentice & Hall 1988). Classical Mechanics, Kibble T W B and Berkshire F H (Imperial College 2004).

Part IB Physics B 31 THERMODYNAMICS

E Eiser

This is a general introduction to classical thermodynamics, followed by an introduction to the statistical representation of gases and the kinetic gas theory. The final part of this course introduces basics of transport phenomena. Examples relevant to Astrophysics and Soft Matter Physics will be discussed.

Fundamentals: Thermodynamic variables; functions of state; zeroth law; concept of temperature; work and heat; 1st law of thermodynamics; heat capacities.

2nd Law and Entropy: Reversible and irreversible changes; Clausius and Kelvin formulations of 2nd law; Carnot cycle and Carnot's theorem; definition of thermodynamic temperature; heat engines, pumps and refrigerators; efficiency; Clausius’ theorem; entropy and its increase; entropy of ideal gas.

Analytical Thermodynamics: Thermodynamic potentials and their uses. Chemical potential. Introduction to Maxwell relations and their applications.

Phase Changes: Real gases and van der Waals’ equation; conditions for equilibrium. Latent heat. Clausius-Clapeyron equation. Gibbs-Duhem relation. Phase rules.

Third Law: Entropy at low temperatures; adiabatic demagnetisation; unattainability of absolute zero.

Kinetic Gas theory: Introduction of Boltzmann distribution; Maxwell-Boltzmann distribution (velocity distribution in gases); pressure and fluxes; barometric height distribution; equipartition theorem; degrees of freedom.

Basic terms & equations in transport phenomena: Momentum - viscosity, energy - heat, mass - concentration gradients. Viscosity and flux in Astrophysics. Flow problems in Soft Matter Physics.

Applications to Simple Physical Problems: Thermodynamics of Radiation. Heat capacity of a vacuum – black body radiation; pressure and energy density. Kirchhoff’s Law. Stefan- Boltzmann Law. Planck’s Law.

BOOKS The course will mainly follow the book “Concepts in Thermal Physics” S.J. Blundell & K.M. Blun- dell (Oxford University Press).

For further reading: “Equilibrium Thermodynamics” Adkins C J (3rd edn CUP 1983). “Thermodynamics and an Introduction to Thermostatistics” H. P. Callen (John Wiley & Sons 1985).

32 Part IB Physics B INTRODUCTION TO COMPUTING

C G Lester

This course in computer programming will take place in Michaelmas. The course will teach the ‘C’ subset of C++. The course strongly takes the view that best way to learn how to write computer programs is to sit in front of a computer and to "have a go". Programming is a skill that (like learning to play a musical instrument) is best learned through direct experience, through practice, by learning from one’s mistakes, by attempting to copy and understand examples etc. It is not a skill that can be absorbed simply by sitting in a lecture theatre and listening to a lecturer. For this reason, the course will mostly be taught through self-guided study in practical classes in which students will work through examples in the course handout. The self-study part of the course will be preceded by two introductory lectures. The purpose of these lectures is to outline the basics tools required to follow the instructions in the course booklet, and to give a very brief introduction to the concept of computer programming. Students must understand that it is not the lecture course that will teach them how to program. Their most important resources for learning will be the handout, the student sitting next to them in the practical class, the practical class demonstrator, the other students on the course, and last but not least printed and on-line reference materials. Anyone attempting to teach themselves to program will benefit strongly from having a C++ reference book beside them at all times (see some suggestions below) and an open web-browser in which to look up examples of code, etc. Students are actively encouraged to discuss what they are doing with others doing the course, to work in pairs or small groups, and to and ask questions of the demonstrators and the people sitting near them in the examples classes. The general structure of the course will be: • Two introductory lectures, followed by practical classes in the MCS (formally PWF) in which the students will work through the self-study guide. Each practical session will have a specific programming task. The aim of the first half of the course is for every student to become familiar with linux, gnuplot, a text editor, elementary C++ programming, and a C++ debugger. In the second half of the course, students will each complete two or three mini-projects. Each mini-project will consist of a core task which all students will have to complete and optional parts introducing more interesting computational/physics ideas.

Assessment The assessment will be weekly. After each practical session, each student will be required to upload work which shows how they solved the tasks described in the handout for that week. (Work may also be handed in early!) Each submission will lead to a simple pass/fail mark for that week. There are no bonus marks for fancy submissions -- the simpler the submission the better. For each project there will be two deadlines - (i) the recommended deadline, and (ii) the extended deadline. The latter will be one week after the former. All students should hand in work by deadline (i) in order to keep pace with the course, but applications for extension to deadline (ii) will be automatically granted when requested to cover problems caused by illness etc. Any work submitted later than the (already extended!) deadline (ii) will not be accepted therefore under any circumstances.

Part IB Physics B 33 Week 1 Computing concepts What a C++ program looks like. Conditionals, loops. Monte Carlo methods. Computing skills Using linux, bash, text editor, C++ compiler, execution. Week 2 Computing concepts Representation of numbers in a computer. . Computing skills Boolean expressions. Relational operators. Simple control structures. C++ debugger. Week 3 Computing concepts Functions. Debugger. Computing skills Defining, declaring, and calling functions. Passing values to and returning values from functions. Using gnuplot. Weeks 4-6 Computing concepts Pointers. Memory allocation. Arrays. Passing arrays to functions. Code- testing.

BOOKS

Any web-search or visit to a book-shop or library will rapidly show that there are hundreds of C and C++ books on the market. Any of them is better than nothing, as all contain important reference material an example programs. Use whatever you have in your college library, or anything owned by "someone on your staircase", as any book is better than nothing. If you can really find no other sources, and want guidance, you could do worse than buy one of the following: Recommended by the 2007 and 2008 lecturer: C++: A Beginner's Guide, Second Edition (Beginner's Guides (McGraw-Hill)) by Herbert Schildt The resource the current lecturer learned C++ from: C++ Primer by Stanley B. Lippman, Josée Lajoie, and Barbara E. Moo, The first and most influential (but not necessarily the best written) book about C++: The C++ Programming Language, Special Edition by Bjarne Stroustrup Everyone needs pocket reference, and it is only £4 on Amazon: C++ Pocket Reference (Pocket Referemce) by Kyle Loudon Likely to be useful: Accelerated C++: Practical Programming by Example (C++ in Depth Series) by Andrew Koenig and Barbara E. Moo Sams Teach Yourself C++ in One Hour a Day by Jesse Liberty, Siddhartha Rao, and Bradley L. Jones

Not about C++ per se, and far beyond what the course requires, but worth reading if the rest of the course is too easy and you want to do "real" object-oriented programming: Design patterns : elements of reusable object-oriented software by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides

Website: The course website for the last academic year may be found at http://www.hep.phy.cam.ac.uk/lester/c++2012/

34 Part IB Physics B MATHEMATICAL METHODS

C A Haniff

The full synopsis is given on p.23 of this course guide.

Part IB Physics B 35 GREAT EXPERIMENTS

A N Lasenby and others

The course runs in the Lent Term, on Mondays at 10, which unfortunately conflicts with both Bio- chemisty & Molecular Biology, and Geology A: students not taking either of these subjects, and taking either or both of Physics A and Physics B, are warmly encouraged to attend.

Full details are given on p.24.

36 Part IB Physics B IB PRACTICAL CLASS – PHYSICS B

W Allison and R T Phillips

The Practical Classes for the IB Physics options (i.e. both the A & B courses) are organized around a set of fourteen experiments, six in the Michaelmas term and eight in the Lent term. Students taking the A, B or both A+B courses undertake different numbers and combinations of these experiments during the year. Candidates taking only the Physics B course will usually undertake a total of 6 experiments during the year (3 in the Michaelmas term and 3 in the Lent term) attending two 3¾ hour long afternoon sessions (over a fortnight) per experiment. Candidates taking both the Physics A and Physics B courses are expected to undertake 6 experiments in the Michaelmas term and 4 experiments in the Lent term, but will complete each of these over the course of a week (usually in one day). They also undertake a longer experimental investigation in groups of four, spread over the final two weeks of the Lent term.

For full details of the classes, see p.38.

Part IB Physics B 37 IB PRACTICAL CLASS – PHYSICS A and B

W Allison and R T Phillips

Candidates taking a single Physics course will usually undertake a total of either 6 or 7 1 experiments during the year (3 in the Michaelmas term and either 3 or 4 in the Lent term) attending two 3¾ hour long afternoon sessions (over a fortnight) per experiment. One experiment must be written up as a Head of Class report.

Candidates offering both Physics courses are expected to undertake 6 experiments in the Michaelmas term and 4 experiments in the Lent term, but will complete each of these over the course of a week (usually in one day). They also undertake a longer experimental investigation in groups of four, spread over the final two weeks of the Lent term. One of the experiments undertaken in the Michaelmas term must be written up as a Head of Class report.

The primary aim of the classes is to provide students with an opportunity to develop the key skills associated with the design and execution of experiments, and with analysing experimental data, hypothesis testing, presenting results and, importantly (especially for theoreticians), assessing others’ experimental results and analyses. Topics covered include a “systems approach” to experimental design, managing noise, offsets and systematic errors, and using experiments to tie down physical phenomena whose theoretical basis is uncertain or unknown – this is the standard situation for a research physicist. For those taking both the A and B courses, presentational skills and team-working also feature in the extended investigation at the end of the Lent term.

A secondary aim of the classes is to demonstrate aspects of, and reinforce the content of, some of the Michaelmas and Lent term lectures.

The following sections outline the full set of 14 experiments available during the year, although students will only ever be expected to undertake a subset of these. Students must refer to the table at the end of this section to determine which experiments they will be required to undertake.

MICHAELMAS TERM: SYSTEMS AND MEASUREMENT

These experiments demonstrate key aspects of “real world” physics, i.e. as an experimentally- driven subject where measurements both validate theories and provide the stimulus for new theoretical developments. Many of the experiments also demonstrate critical features of the physics introduced in the Physics A Experimental Methods, Oscillations, Waves and Optics, and Electro- magnetism lecture courses. Students will usually be expected to work in pairs, with the classes running from week 2 through week 7 of the term.

There are six experiments in total, each lasting about six hours, as follows.

[1] Basic skills: Using a PicoScope; measuring input and output impedances, frequency response and phase shift; ensuring the measuring device does not affect the measurement; using an operational amplifier.

1 Students taking only Physics A undertake 7 experiments, whereas students taking only Physics B undertake 6 experiments since they also take an assessed computing course. 38 Part IB Practical Work (Physics A & B) [2] Linear systems and feedback: An operational amplifier is used to explore various linear systems, including voltage amplifiers and integrators. The system concepts of negative and positive feedback are investigated.

[3] Non-linear systems: An analogue multiplier will be used to explore the properties of nonlinear systems. Frequency doubling, mixing and de-modulation will be investigated.

[4] Hysteresis: Building a simple magnetometer and investigating hysteresis in three magnetic materials.

[5] Signals and noise in an optical link: An optical communication link is constructed. Phase-sensitive detection is used to extract the signal in the presence a very high level of con- taminating noise.

[6] Twangs and clicks (data sampling and Fourier methods): An investigation of sampling, aliasing and Nyquist’s theorem, followed by the design, construction and use of apparatus to test the validity of a model developed to explain the properties of a tuning fork.

LENT TERM: WAVES AND OPTICS – First ¾ of term

The first part of the Lent term focuses on investigations that continue the development of the skills associated with the design, execution, and interpretation of experiments. Additionally, they provide further opportunities to demonstrate some of the relevant physical principles developed in the Physics A and B lecture courses.

Students taking only one of Physics A or Physics B will be expected to work in pairs and attend for two afternoon session on the same day on two consecutive weeks per experiment. Pairs will be expected to start these “main” experiments in either week 2, week 4 or week 6 so that at most three from the list below can be undertaken. All single subject students will also be expected to undertake the short initial class “Key experimental techniques” in week 1 starting at 2pm.

There will be no attendance for single subject students in week 8, and they will not undertake the extended investigation.

Students taking Physics A with Physics B will be expected to work in pairs (or triples – this will depend on the class size) and will undertake each of their “main” experiments in a single weekly session. Students will be expected to sign up to undertake three main experiments from the list below over the course of weeks 2 through 5. This will allow one “week off”. All double subject students will also be expected to undertake the short initial class “Key experimental techniques” in week 1 starting at their usual 10am or 2pm time.

There will be no attendance for double subject students in week 6, but they will undertake an extended investigation in weeks 7 and 8 (see below for details).

In this first part of the term seven experiments will be run, the first taking roughly 3½ hours, and the remainder about seven hours, as follows.

[7] Key experimental techniques: Developing observational skills: descriptive skill, using a PicoScope for data acquisition and laptop-based software for data analysis, observation as a tool for developing theories, review of random and statistical errors and their diagnosis, practice with Excel.

[8] Fraunhofer diffraction of light: This is investigated experimentally using a laser and a variety of apertures. Quantitative analysis of the measurements is used as a sensitive test of this diffraction theory. The experiment also provides a visualisation of Fourier transforms and helps develop intuition for these and the concept of spatial filtering.

Part IB Practical Work (Physics A & B) 39 [9] Ultrasonic waves: This experiment is designed to investigate the propagation of ultrasonic waves in air and other fluids. Not only is it possible to examine the standard wave-like behaviour of ultrasound (reflection, diffraction, etc.), but also the experiment demonstrates how ultrasound can be used to probe the kinetic properties of materials.

[10] Waves in liquids: A wave tank is used to study the propagation of waves at the interface layer between two liquids. The dispersive nature of the system makes it particularly interesting. The propagation and spectral structure of wavepackets is also studied.

[11] Fresnel diffraction of light: This experiment demonstrates important features of Fresnel diffraction and allows a quantitative verification of Fresnel theory. It also allows the investigation of off-axis effects which are difficult to analyse theoretically.

[12] Microwaves and waveguides: A solid-state device, a Gunn diode, is used to generate microwaves which are used to investigate a wide variety of electromagnetic phenomena. Propaga- tion in free space, in materials and along waveguides is studied.

[13] Interferometers and spectroscopy: Interferometry is a very important tool for spectroscopy and one aim of this experiment is to demonstrate the great accuracy that can be achieved. Two types of interferometer are used, a Michelson interferometer and a Fabry-Perot etalon. A variety of effects is demonstrated, and an introduction provided to the practical problems of setting up and calibrating high precision instrumentation.

LENT TERM: EXTENDED INVESTIGATION – Last ¼ of term

In weeks 7 and 8 of the Lent term students taking both Physics A and Physics B will be expected to undertake a more open-ended and less structured investigation of a single topic over two consecutive weekly sessions. These will be executed in randomly-selected groups of four. The assessment of the investigation will primarily be via an hour long oral and slide-based presentation to a Head of Class in which all the members of the group will be expected to participate. This presentation will take place at the start of the Easter term.

[14] Extended investigation: The topic of the investigation will change from year to year.

CHOICE OF EXPERIMENTS in Lent Term

The selection of experiments available for students taking Physics A or B alone and students taking both the Physics A and Physics B courses is summarized in the table below. Experiments marked with a tick () are compulsory. Where a box is greyed-out in a particular column, that experiment is not available for the particular combination of subjects. Experiments identified with a report icon ( ) can be chosen from to write a Head of Class report.

40 Part IB Practical Work (Physics A & B) Physics A only Physics B only Physics A+B (7 experiments (6 experiments (11 experiments in total) in total includ- in total including ing either op- three from ex- tion 1 or option periments 9-13) 2) Michaelmas Term [1] Basic skills    [2] Linear systems and feedback    [3] Non-linear systems  [4] Hysteresis   [5] Signal and noise in an optical link  [6] Twangs and clicks   Lent Term – first ¾ of term [7] Key experimental techniques    [8] Fraunhofer diffraction of light   [9] Ultrasonic waves   [10] Waves in liquids  Option 1 Do three out of [11] Fresnel diffraction light five [12] Microwaves and waveguides Option 2 [13] Interferometry and spectroscopy  Lent term – last ¼ of term [14] Extended investigation 

In all cases, students must attend the first class of the Term on their pre-assigned day of the week at which time the detailed timetable and sequence of experiments will be determined. Students must do all the experiments checked in the relevant column of the table above.

HEAD OF CLASS REPORTING

All students are required to write up one of the experiments they have performed in the form of a formal Head of Class write-up. Students taking only the Physics A or only the Physics B course may choose to submit a Head of Class write-up in either the Michaelmas or Lent Terms. The report must be on one of the experiments marked with the report icon ( ) in the table above. Students taking both the Physics A and the Physics B course must submit their Head of Class write-up in the Michaelmas term, again on one of the experiments marked with the report icon in the right-hand column.

Each write-up will be assessed by a Head of Class and the marks awarded will count towards the end of year assessment. Students who undertake the extended investigation in the Lent term must also present the results of their investigation in the form of an hour-long oral and slide-based presentation to a Head of Class at the beginning of the Easter Term. As for the Head of Class write-up, this presentation will be assessed by the Head of Class and the marks awarded will count towards the end of year assessment.

Advisory note to candidates taking only the Physics B course:

The practical work in the Michaelmas and Lent Terms draws heavily on lecture material presented in the Physics A course in the Michaelmas Term: students are advised to attend at least the Experimental Methods lectures from the Physics A course for the necessary background to the practical classes.

Part IB Practical Work (Physics A & B) 41 Part II Physics

Comments may be sent to [email protected] Enquiries/queries: [email protected]

Wednesday of Full Term (9th October 2013) at 6.1 THE THREE- AND FOUR-YEAR 9.30 am in the Pippard Lecture Theatre at COURSES IN PHYSICS the Cavendish Laboratory. Part II Physics contains work of two types: Core It is assumed that all students taking Part II Phys- lectures in the Michaelmas term and Options lec- ics will have attended both Physics A and Physics tures in the Lent/Easter terms, which are exam- B in Part IB (or equivalent courses in the Mathe- ined at the end of the year in the usual way, and matics Tripos). units of ‘Further Work’, which are assessed during There are two paths to graduating in Physics, both the year. Students take three or more of the leading to a wide range of career options. Both Lent/Easter lecture courses together with at least groups of students take the same course in the three units of Further Work. third year. The paths are: We do not expect any student to take more than  3-year course leading to B.A. hon- the minimum number of units of work in any ours degree: this path is designed for category. The great majority of students will find students with a deep interest in the sub- the workload demanding even at this level. We ject but who do not intend to become pro- recognise, however, that some students may have fessional physicists. It is a challenging good reasons for wishing to take additional course and exposes students to core areas courses for credit. Marks for all examination pa- of physics at an advanced level. Students pers sat will appear on the students’ University on this path will graduate at the end of the transcripts. Within any part of the examination Part II course with a B.A. (options courses, Further Work) the best results meeting the minimum requirement will count to-  4-year course leading to an M.Sci. wards the class for the year. honours degree (master of Natural Sciences), together with a B.A. hon- The aim of the Michaelmas Term lecture courses ours degree: students who wish to pur- is to complete basic instruction in physics. In this sue a professional career in physics (for term, there are four core courses: example in academic or industrial re-  Advanced Quantum Physics; search) take the usual third year Part II but do not graduate at the end of the third  Relativity; year. Subject to requisite funding, college  Optics and Electrodynamics; approval and achievement of a 2:1 result or better in Part II Physics students are  Thermal and Statistical Physics. admitted to take Part III Physics in their In the Lent and Easter terms, four option courses fourth year. Both B.A. and M.Sci. degrees are offered, introducing broad areas of physics: are conferred at the end of this fourth year.  Astrophysical Fluids; The Part II Physics course is very flexible, and can  Particle and Nuclear Physics; range from strongly experimental to highly theo-  Quantum Condensed Matter; retical physics, with a range of specialist options. There are possibilities for substantial independent  Soft Condensed Matter. work and for experience of industrial research. All students are also expected to take the course There is no limit on the number of students taking on Computational Physics, which is assessed by a Part II Physics and we usually have about 150 stu- series of short exercises. In addition, an extended dents, the largest class in any Part II Natural Sci- Computational Physics project is available as one ence subject. of the optional units of Further Work.

6.2 OUTLINE OF THE COURSES The remainder of the Further Work offers a free choice. Students may select an experimentally- The detailed timetable is available online biased course by carrying out up to two experi- http://www.phy.cam.ac.uk/teaching/lectures.php mental investigations (E1 and E2), each lasting The course begins with a meeting on the first 42 Part II Physics two weeks. Alternatively, there are two possible dividual experiments starting on the first, third courses in Theoretical Physics (TP1 and TP2), and fifth Mondays in Term. The details of these consisting of lectures plus examples classes, which sessions will be announced during registration at run respectively in the Michaelmas and Lent the start of term. E1 is assessed during the terms. We expect that almost all students will of- Michaelmas Term so that any appropriate advice fer at least one of E1 and TP1. Further optional and constructive criticism can be given before a elements of Further Work are a Computing Pro- decision has to be taken on whether or not to offer ject, Research Review, Physics Education or a E2. Students opting for E2 only after taking the Long Vacation Project. All units of further work TP1 examination (see Section 6.3.3) are likely to are outlined in Section 6.3 and a table setting out be allocated to E2b or E2c. No student is allowed the range of options is given on p.45. to offer more than two units of experimental investigation. There are also two unexamined courses, on Topics in Astrophysics and Concepts in Physics. The experiments available in Part II are offered by the experimental research groups from within the 6.3 FURTHER WORK Department. A list is given on p 66 below. The ex- Of the optional Further Work, note that not more periments give you the chance to develop profes- than two Experiments may be offered. Other rules sional ability, both in performing a substantial for choosing Further Work are set out in Section experiment and in relating experiment to theory. 6.6 on Examinations and in the Table on page 44. Most students find these experiments more demanding and more satisfying than the short ex- Students will be contacted by e-mail and should periments of the Part I classes. They are assessed register on-line via the teaching web pages by a Head of Class write up followed by an oral http://www.phy.cam.ac.uk/teaching/ before the examination. start of Michaelmas Term and to give an indication of which units of Further Work they intend to complete. In particular, they will be asked to 6.3.3 Courses in Theoretical Physics make a provisional choice of experiments for E1 and E2 if they intend to take those options. These The Theoretical Physics Courses are challenging arrangements may be modified at the registration courses aimed at students who find mathematics meeting at the beginning of term. Students wish- relatively easy and who have a strong interest in ing to change their choice during the course of the the mathematical description of physical systems. year (for example those wishing to take E2 instead The majority of students taking these courses will of TP2 in light of their TP1 results) should contact have taken Part IB Mathematics for NST, but the the Teaching Office. Mathematical Methods course offered as part of Physics A and B in Part IB provides nearly all of The arrangements for submitting and assessing the necessary background. Usually the mark dis- Further Work are described in 6.6.4 below and in tributions for these courses have a tail of low the Course Synopses later in this handbook. marks obtained by students who would probably 6.3.1 Computing have scored higher marks if they had done experimental work. All students are expected to attend the Computa- tional Physics lectures in Lent term, which build Theoretical Physics Course TP1 is taken in the on the Part IB C++ course. Associated with the Michaelmas Term and students take a written test lectures are Computing exercises which are paper at the start of the Lent Term. The results equivalent to 0.2 units of work, and are compul- will be made available to guide your choice of fur- sory for all Part II Physics students. In addition, ther work for the Lent term. A second Theoretical students may elect to offer an extended Comput- Course, TP2, is taken in the Lent Term and tested ing Project, which will involve analysing a physics at the start of the Easter Term. TP1 and TP2 each problem, and writing a program to solve it. This count for one unit of Further Work. As well as project is optional, and counts as one unit of Fur- lectures, four examples classes are given in each of ther Work. Further details are given on p.62. TP1 and TP2. Detailed synopses are given on p.63. 6.3.2 Experimental Investigations

Each experiment will involve 30 to 40 hours work and will be equivalent to one unit of Further Work. The E1 and E2 sessions are run in the Michaelmas and Lent terms respectively, with in-

Part II Physics 43 Part II Physics Core and Options Schemes

Lectures Course Half Subject PHYSICS Michaelmas Term Core courses 18 Thermal and Statistical Physics  24 Relativity choose  24 Advanced Quantum Physics 2  16 Optics and Electrodynamics  Lent/Easter Terms Option Courses 8 Computational Physics FW (0.2 units)   24 Astrophysical Fluid Dynamics 22 Particle and Nuclear Physics choose choose 22 Quantum Condensed Matter 1 3 or 4 22 Soft Condensed Matter

Further Work (FW), (1 unit ≈ 1.5hrs examination) FW units Research Review 1 † Physics Education (limited numbers) 1 Computational project 1 choose choose Experiment E1 & E2 1 each 2 3 or more Theory TP1 & TP2 1 each Long Vacation project (approval required) 1 FW units 2 3+ Exam Units 3 7+ Notes: % FW 40% 30% Papers: 2hrs for each course (≡ 4 Units FW) † Half Subject Physics students choose a Research Review as the topic for their dissertation in Part II Physical Sciences.

44 Part II Physics 6.3.4 Research Review Details of the nature and scope of this course are given at length in the course synopsis on page 71 A Research Review is equivalent to one unit of below. Numbers are restricted and students wish- Further Work, and consists of a review (of 3000 ing to take part must attend the introductory ses- words max.) on some area of physics, approved in sion between 2-5pm on Thursday 10th October advance. Such a review must have a Supervisor. 2013. In about the sixth week of the Lent Term supervisors will organise a meeting at which students will 6.4 SUPERVISIONS AND EXAM- have the chance to present their interim work to PLES CLASSES other students working on reviews in similar ar- Supervision for Part II is organised by the De- eas and their supervisors. As well as providing a partment on behalf of the Colleges. During the chance to obtain feedback this should ultimately Michaelmas term Physics students are supervised raise the standard of the submitted work. You re- in all four core lecture courses, and Half Subject ceive 5% of the available marks for the Research Physics students in two. Supervisions for these Review for giving the presentation (irrespective of courses will be allocated automatically according its quality). Research Reviews are assessed by two to the option for which you are registered. staff members with a short oral examination early in the Easter Term. This examination will usually In the Lent term students choose their supervi- begin with a short oral presentation. sions according to their choice of subjects for examination. The sign-up procedure is web-based, Further details are given on p.69. and you will be notified by email in plenty of time. 6.3.5 Long-Vacation Work We ask you to sign up by 2.00 pm on the last Fri- day of Michaelmas Full Term, so that arrange- Scientific work during the Long Vacation prior to ments can be made during the Christmas your third year can count as project work worth vacation. Obviously this does not allow you to one unit of Further Work. The full details can be sample the courses: if you subsequently decide obtained from Dr Padman ([email protected], As- that you wish to change options, then please visit trophysics Group), but you must get your pro- or email the Teaching Office to request a change posal approved in advance, before the end of the of supervisor. preceding Easter Term. Forms are available from the Teaching Office. You will be required to name The number of supervisions for each course is in advance a suitably qualified on-site supervisor summarised in the table overleaf. who is willing to write retrospectively to Dr Pad- Supervision will normally be in groups of three, man describing the work you have done and giv- although you may occasionally find yourself in a ing an assessment of your effectiveness. Normally two or a four, to allow supervisors to accommo- the programme must be of at least two months date odd numbers or students who are wildly duration and must include a substantial element mismatched in their ability in a particular subject. of independent or original work. It is important You must be prepared to work much more that the project includes a significant amount of independently than at Part I. Difficulties that physics and is not, for example, simply a series of arise in lectures are often more conveniently dis- routine measurements or entirely devoted to cussed with the lecturers themselves at the end of computer programming. lectures, or by arrangement at other times Vacation projects within the University may be of- You must take responsibility for ensuring that the fered through the Undergraduate Research Op- supervisions go as far as possible in meeting your portunities Programme (UROP). See needs. Supervisors are usually willing within rea- http://www.phy.cam.ac.uk/teaching/UROPS/uro sonable limits to be flexible about the detailed ar- p.php for details. Some of these projects may be rangements. You should expect to be asked to suitable as assessed Long-Vacation Work. The hand in work for each supervision, in time for teaching web pages http://www your supervisor to look through the work and teach.phy.cam.ac.uk/teaching/vacWork.php identify any potential problems. However, the might offer some useful suggestions. quantity and complexity of the work at this level 6.3.6 Physics Education means that supervisors may be unable to provide the detailed personal marking that you experi- The Physics Education course counts as one unit enced in Parts IA and IB of further work. It offers the possibility of devel- Supervisors may range from established lecturers oping and presenting teaching material in a sec- with long teaching experience to relatively inexpe- ondary school. It develops a wide range of rienced graduate students. New supervisors are transferable skills and provides a real opportunity expected to seek advice on supervising, to attend to explore the possibility of a career in teaching. the courses provided by the University, and to Part II Physics 45 commit to the necessary preparation for each su- on some Wednesdays. Part II students are also pervision. However, experience is the only real welcome at the many Research Seminars and teacher, and inevitably some supervisors will be other lectures in the Department, particularly more confident than others, particularly at an- those organised by the Cambridge Physics Centre. swering subtle and unexpected questions. These are advertised on notice boards, and on the Cavendish groups’ web pages.

SUPERVISIONS IN PART II (2013-14) 6.6 THE EXAMINATION

Half PHYSICS 6.6.1 Examiners’ Notices Subject MICHAELMAS Specific information about the examination is Thermal and Statistical 4 given in notices put up on the Part II notice board Electrodynamics & Light Choose 2 4 outside the Pippard Lecture Theatre. You should Relativity 4 make sure that you read these regularly. Adv. Quantum Physics 4 6.6.2 The Written Papers for Part II SUBTOTAL 8 16 The exact content of each Paper is a matter for the LENT relevant Examiners. Each of the core and op- Astrophysics tional lecture courses is examined in a separate Particle & Nuclear Phys- choose 1 4 in each of two hour paper. ics 3 chosen Quantum Condensed subject subjects 6.6.3 Requirements Matter Soft Condensed Matter The written examinations consist of the core lecture course papers, plus three or four of the op- SUBTOTAL 4 12 tion lecture course papers. In addition to the TOTAL 12 28 computing exercises, three or more other units of Further Work must be offered and may be drawn from the various choices described in Section 6.3 Without an influx of new supervisors the system (see the Table on p.44). will rapidly decay, so please be understanding. If 6.6.4 Examination Entries you do have problems with your supervisor that cannot be solved by direct two-way discussion, You are required to make a preliminary indication please contact your Director of Studies in the first of which papers you intend to offer when you fill instance. If he or she feels that intervention is in your exam entry on CamSIS at the start of warranted, s/he should contact the Supervisions Michaelmas term. You will then be required to coordinator (currently Dr Rachael Padman). specify which final combination of papers you intend to offer by modifying the exam entry during 6.5 NON-EXAMINED WORK Lent term, in liaison with your College Tutorial There is a non-examinable course of 24 lectures in Office. Any questions on completing the exam en- the Michaelmas term on Topics in Astrophysics. try should be discussed with your Director of These lectures should be interesting for all stu- Studies. dents and are intended to provide valuable back- 6.6.5 Submission of Further Work ground for those who are interested in pursuing Astrophysical courses in Part III When any piece of Further Work is submitted it There is a non-examinable course of 8 lectures in should be in a complete and final form. the Lent term on Concepts in Physics, intended to Students are permitted to submit more than the place in perspective some major themes of phys- minimum number of units of Further Work. Once ics, to sketch connections between them and to a piece of Further Work has been submitted, it investigate unresolved questions. Attendance is will be marked: the best marks for the required strongly encouraged for all students. minimum number of units will count towards the Open Days (open to Part II and Part III students) class, but all marks will appear in the markbook, will be held during the year and are intended to and on the transcript. give an idea of the range of current research in the TP1 and TP2 are assessed by written tests during laboratory. Dates are given on-line and posted on the year. Once you have entered the room for the the Part II and Part III notice boards. TP1 or TP2 test the unit of Further Work will Undergraduates are encouraged to attend the count towards the final total. Cavendish Physical Society lectures, at 4.00 pm 46 Part II Physics In accordance with the University’s regulations, combined with a subject from Part IB not previ- work submitted after the advertised deadline will ously taken. not count towards your final examination mark, Candidates offer unless the Department grants an extension of time on the grounds that there are mitigating i) Two of the core lecture course papers. circumstances. Any application for such an ex- ii) One of the option lecture course papers. tension should be made by your college Tutor or Director of Studies to the Director of Under- iii) Computing exercises and two units of Further graduate Teaching, c/o Teaching Office, Caven- Work (not including a Research Review). dish Laboratory, (teaching- In addition, Physical Sciences students must offer [email protected]). In such circumstances, a dissertation on a topic consistent with their Half you should submit the work as soon as possible Subject. For Half Subject Physics this dissertation after the deadline. will be on a topic from those offered for Research The Regulations require that assessed Records of Reviews, but with a word limit of 5000 (rather Further Work be submitted to the Examiners than 3000 for a Research Review. through the Head of the Department; this hap- You will be required to specify which combination pens automatically after assessment. of papers you intend to offer by the third week of There is a list of important dates at the end the Lent Term. of this section. Vacation work may be arranged as described in Section 6.3.6, and, if approved as there detailed, 6.7 HALF SUBJECT PHYSICS may be counted as one unit of Further Work. Half Subject Physics is part of Natural Sciences The arrangements for submitting Further Work Part II Physical Sciences. It comprises about half are the same as those for Part II Physics candi- of the work load of Part II Physics, and may be dates.

Part II Physics 47 6.8 SOME IMPORTANT DATES Note: This list is not exhaustive, and may be superseded by announcements on the TIS. In particular please note that those student wishing to progress to Part III will need to make their choice of Part III project in Lent term 2014. Further details will be announced on the TIS. Tuesday 8th October 2013 Start of Michaelmas full term Wednesday 9th October 2013 9.30 General Registration (Pippard Lecture Theatre, Cavendish Laboratory) Monday 14th October 2013 14.00 Briefing for E1a, in relevant laboratory Monday 14th October 2013 16.00 Vacation work report deadline Monday 14th October 2013 14.00 First TP1 lecture Wedn 16th October 2013 14.00 First TP1 examples class Friday 25th October 2013 17.00 E1a laboratories close Monday 28th October 2013 14.00 Briefing for E1b, in the relevant laboratory Wed 30th October 2013 16.00 E1a report deadline Friday 1st November 2013 Research review topics preliminary selection deadline Friday 8th November 2013 17.00 E1b laboratories close Monday 11th November 2013 14.00 Briefing for E1c, in the relevant laboratory Wed 13th November 2013 16.00 E1b report deadline Monday 18th November 2013 14.00 Last TP1 lecture Friday 22nd November 2013 17.00 E1c laboratories close Wed 27th November 2013 16.00 E1c report deadline Wed 27th November 2013 14.00 Last TP1 examples class Friday 6th December 2013 End of Michaelmas full term Tuesday 14th January 2014 Start of Lent full term Wed 15th January 2014 TP1 examination Thursday 16th January 2014 12.00 First TP2 lecture Monday 20th January 2014 14.00 Briefing for E2a, in relevant laboratory Tuesday 28th January 2014 14.00 First TP2 examples class Friday 31st January 2014 17.00 E2a laboratories close Monday 3rd February 2014 14.00 Briefing for E2b, in the relevant laboratory Wed 5th February 2014 16.00 E2a report deadline Friday 14th February 2014 17.00 E2b laboratories close Monday 17th February 2014 14.00 Briefing for E2c, in the relevant laboratory Wed 19th February 2014 16.00 E2b report deadline Thursday- 20th – 26th February 2014 Presentations of Research Reviews (will be organised Wed by your supervisor) Friday 28th February 2014 17.00 E2c laboratories close Wed 5th March 2014 16.00 E2c report deadline Tuesday 11th March 2014 14.00 Last TP2 examples class Friday 14th March 2014 End of Lent full term Tuesday 22nd April 2014 Start of Easter full term Wed 23rd April 2014 TP2 examination Monday 28th April 2014 16.00 Computing Report deadline Monday 28th April 2014 16.00 Research Review deadline Monday 28th April 2014 16.00 Physics Education deadline Tuesday- 29th April Oral examinations on Research Reviews Monday - 12th May 2014 (will be organised by your supervisor) Friday 6th June 2014 Deadline for obtaining approval for Part II students to do Long-Vacation Work for submission as part of Part III Friday 13th June 2014 End of Easter full term

48 Part II Physics 6.9 LECTURE LIST

PART II PHYSICS

PHYSICAL SCIENCES: HALF SUBJECT PHYSICS

Departmental Contact: Helen Marshall: E-mail: [email protected] Course Website: http://www.phy.cam.ac.uk/teaching/

Students taking Part II Physics must take all four Core courses in the Michaelmas Term, three or more of the Options courses in the Lent and Easter Terms, and Computational Physics. They must in addition take three or more courses from Physics Education, Theoretical Op- tions and Other Further Work. There is a test (under exam conditions) of the material of the Theoretical Options at the start of the term following that in which each block, TP1 and TP2, is given. All students are recommended to attend the Non-examinable courses Concepts in Physics and Current Research Work in the Cavendish Laboratory.

Students taking Half Subject Physics as part of Part II Physical Sciences will take any two of the Core courses in the Michaelmas term and any one of the Options courses in the Lent and Easter terms. Candidates also take two units of further work selected from Theoretical Op- tions, Physics Education and Experiments or Long Vacation Project. A prior knowledge of Physics equivalent to the material covered in Part IB Physics A and Part IB Physics B will be assumed.

The course will begin with a meeting on the first Wednesday of Full Term (9 Oct.) at 9.30 a.m. in the Pip- pard Lecture Theatre.

For the up-to-date lecture list please go to: http://www.phy.cam.ac.uk/teaching/lectures.php

Part II Physics 49

ADVANCED QUANTUM PHYSICS

N R Cooper

Review of Quantum Physics: Postulates of quantum mechanics, operator methods, time- dependence, symmetry. Solutions to the Schrödinger equation in one dimension. Angular momentum and spin; matrix representations.

Motion of charged particle in electromagnetic field: normal Zeeman effect; diamagnetic hydrogen; gauge invariance; Aharonov-Bohm effect; Landau levels.

Approximate Methods: Time-independent perturbation theory, first and second order expansion; Degenerate perturbation theory; Stark effect; nearly free electron model. Variational method: ground state energy and eigenfunctions; excited states. The WKB method: bound states and barrier penetration.

Identical particles: Particle indistinguishability and quantum statistics; free particle systems;effects of interactions.

Atomic and molecular structure: Revision of Hydrogen Atom. Fine structure: relativistic corrections; Spin-orbit coupling; hyperfine structure. Multi-electron atoms: LS coupling; Hund’s + rules; Zeeman effect. Born-Oppenheimer approximation; H2 ion; molecular orbitals; H2 molecule; ionic and covalent bonding.

Time-dependent perturbation theory: Two-level system, Rabi oscillations, Magnetic resonance. Perturbation series, Fermi’s Golden rule, scattering and the Born approximation. Radia- tive transitions, dipole approximation, spontaneous emission and absorption, stimulated emission, Einstein’s A and B coefficients, selection rules; Cavity rate equations and lasers.

Elements of quantum field theory: Quantization of the classical atomic chain; phonons; rules of field quantization and quantum electrodynamics; number states, coherent states, nonclassical light.

BOOKS Quantum Physics, Gasiorowicz S (2nd edition Wiley, 1996; 3rd edn Wiley, 2003) Quantum Mechanics, Non-relativistic theory vol. 3, Landau, L D and Lifshitz L M, (3rd edition Butterworth-Heineman, 1981) Quantum Mechanics, F. Schwabl (Springer, 4th edition, 2007) Quantum Mechanics, Bransden B H and Joachain C J (2nd edition Pearson, 2000) The Physics of Atoms and Quanta, Haken H and Wolf H C (6th edition Springer, 2000) The Principles of Quantum Mechanics Shankar R (2nd edition Springer, 1994) Problems in Quantum Mechanics, Squires G L (CUP 1995)

50 Part II Physics OPTICS AND ELECTRODYNAMICS

H Sirringhaus

Note that the later parts of this course depends on material from the Part II “Relativity” course, which runs in parallel with this in the Michaelmas Term.

Electromagnetic Waves and Optics: Revision of Maxwell’s equations. Light as an EM wave. Polarization and partial polarization. Light in media; anisotropic media; polarizers and wave- plates; optical activity; Faraday rotation. Jones matrices. Layered media; photonic structures. Temporal and spatial coherence.

Electrodynamics: Vector potential A. Calculation of A in simple cases; Aharonov-Bohm effect; Maxwell’s equations in terms of A and ; choice of gauge. Wave equations for A and ; and general solution; retarded potentials.

Radiation: Time-varying fields and radiation. Hertzian dipole; power radiated including angular distribution; magnetic dipoles. Properties of antennas: effective area; radiation resistance; power-pattern. Half-wave dipole. Antenna arrays. Scattering: cross-section; Thomson and Rayleigh scattering; denser media and the structure factor.

Relativistic Electrodynamics: Charges and currents; 4-current; 4-potential; transformation of E and B; covariance of Maxwell’s equations; invariants of the EM field; energy and momentum of the EM field; magnetism as a relativistic effect.

Radiation and relativistic electrodynamics: fields of a uniformly moving charge; Čerenkov radiation; accelerated charges; Larmor and Liénard formulæ; cyclotron and synchrotron radiation; Bremsstrahlung.

BOOKS

Optics, Hecht E (4th edn Addison Wesley 2002) Optical Physics, Lipson S G, Lipson H & Tannhauser D S (3rd edn CUP1995) Electromagnetic Fields and Waves, Lorrain P & Corson D R (3rd edn Freeman 1998) Classical Electrodynamics, Jackson J D (3rd edn Wiley 1998)

Part II Physics 51 RELATIVITY

M P Hobson

Foundations of special relativity: Inertial frames, spacetime geometry, Lorentz transformations, spacetime diagrams, length contraction and time dilation, Minkowski line element, particle worldlines and proper time, Doppler effect, addition of velocities, acceleration and event horizons in special relativity.

Manifolds, coordinates and tensors: Concept of a manifold, curves and surfaces, coordinate transformations, Riemannian geometry, instrinsic and extrinsic geometry, the metric tensor, lengths areas and volumes, local Cartesian coordinates, tangent spaces, pseudo-Riemannian geometry, scalar, vector and tensor fields, basis vectors, raised and lowered indices, tangent vectors, the affine connection, covariant differentiation, intrinsic derivative, parallel transport, geodesics.

Minkowski spacetime and particle dynamics: Cartesian inertial coordinates, Lorentz transformations, 4-tensors and inertial bases, 4-vectors and the lightcone, 4-velocity, 4-acceleration, 4-momentum of massive and massless particles, relativistic mechanics, accelerating observers, arbitrary coordinate systems.

Electromagnetism: the electromagnetic force, the 4-current density, the electromagnetic field equations, the electromagnetic field tensor, the Lorentz gauge, electric and magnetic fields, invariants, electromagnetism in arbitrary coordinates.

The equivalence principle and spacetime curvature: Newtonian gravity, the equivalence principle, gravity as spacetime curvature, local inertial coordinates, observers in a curved spacetime, weak gravitational fields, intrinsic curvature, the curvature tensor, the Ricci tensor, parallel transport, geodesic deviation, tidal forces, minimal coupling procedure.

Gravitational field equations: the energy-momentum tensor, perfect fluids, relativistic fluid dynamics, the Einstein equations, the weak field limit, the cosmological constant, particle motion from the field equations.

Schwarzschild spacetime: static isotropic metrics, solution of empty-space field equations, Birkhoff’s theorem, gravitational redshift, trajectories of massive particles and photons. Singulari- ties, radially infalling particles, event horizons, Eddington-Finkelstein coordinates, gravitational collapse, tidal forces, Hawking radiation.

Experimental tests of general relativity: precession of planetary orbits, the bending of light, radar echoes, accretion discs around compact objects, gyroscope precession.

Friedmann-Robertson-Walker spacetime: the cosmological principle, comoving coordinates, the maximally-symmetric 3-space, the FRW metric, geodesics, cosmological redshift, the cosmological field equations.

Kerr spacetime: the general stationary axisymmetric metric, the dragging of inertial frames, stationary limit surfaces, event horizons, the Kerr metric, structure of a rotating black hole, trajectories of massive particles and photons, Penrose process.

Linearised gravity and gravitational waves: weak field metric, linearised field equations, Lorenz gauge, wave solutions of linearised field equations.

Topics in italics are non-examinable, and might be omitted.

52 Part II Physics BOOKS

General relativity: an introduction for physicists, Hobson M P, Efstathiou G P & Lasenby A N (CUP 2005). This covers all parts of the course.

Relativity: special, general and cosmological, Rindler W (OUP 2001). Good for the concepts and methods. Provides a lot of physical and geometrical insight.

Introducing Einstein's Relativity, d'Inverno R (OUP 1992). Provides a clear description covering most of the gravitation course material.

Gravity: an introduction to Einstein’s general relativity, Hartle J B (Addison Wesley 2003). A clear introduction that does not rely too much on tensor methods.

Spacetime and geometry, Carroll S M (Addison Wesley 2004). A very thorough, yet highly readable, introduction to general relativity and the associated mathematics

General theory of relativity, Dirac P A M (yes, that Dirac…!) (Princeton University Press 1996). A short and well-argued account of the mathematical and physical basis of general relativity. Proba- bly only useful once you already understand the subject.

Part II Physics 53 THERMAL AND STATISTICAL PHYSICS

W A Allison

Introduction and revision of Thermodynamics: The ideal gas; the van der Waals gas; equations of state; phase diagrams. Thermodynamic variables and potentials. Thermodynamic equilibrium in closed systems, maximum entropy; open systems and availability – relation to thermodynamic potentials and to the probability of a state

Fundamentals of statistical mechanics: Principle of equal equilibrium probability; microcanonical, canonical and grand canonical ensem- bles; partition function and grand partition function – relation to thermodynamic potentials and variables; maximisation of partition function. Paramagnetic salt in an external field; ensemble of simple harmonic oscillators.

Classical ideal gas: Counting of states in the phase space; equipartition theorem; indistinguishability; ideal gas in the canonical ensemble; additional degrees of freedom and external potentials; chemical reactions and chemical equilibrium. Grand partition function; density series expansion; p-T ensemble; -p- T ensemble; ideal gas in the grand canonical ensemble

Quantum statistical mechanics: Quantum to classical crossover; Bose-Einstein and Fermi-Dirac statistics; quantum states of an ideal gas. The ideal Fermi gas; low-temperature limit; entropy and heat capacity of fermions of at low temperatures. The ideal Bose gas; Bose-Einstein condensation. Black-body radiation, phonons and spin waves

Classical interacting systems: Liquids; radial distribution function; internal energy and equation of state; pair interaction and virial expansion; van der Waals equation of state revisited. Mixtures and mixing entropy; phase separation; phase diagrams and critical points. Phase transformations; symmetry breaking and order parameters; the Ising model; the Landau theory of phase transitions; 1st and 2nd order transitions, critical points and triple points; transitions in external fields; critical behaviour and universality

Fluctuations and stochastic processes: Fluctuations in thermodynamic variables; probability distribution of fluctuations; fluctuations at critical points. Thermal noise; Brownian motion; stochastic variables and Langevin equation; fluctuation-dissipation theorem. Probability distribution and simple diffusion; diffusion in external potentials; the Kramers problem; generalised diffusion equations

BOOKS

Equilibrium Thermodynamics, Adkins (3rd edn CUP 1983). Concepts in Thermal Physics, Blundell and Blundell (Oxford 2006) Introductory Statistical Mechanics, Bowley & Sanchez (Oxford 1996). Statistical Physics (Course of Theoretical Physics, v.5), Landau & Lifshitz (Pergamon 1980) Brownian Motion, Mazo (Oxford 2002)

54 Part II Physics ASTROPHYSICAL FLUID DYNAMICS

D Sijacki

Fluids are ubiquitous in the Universe on all scales. As well as obvious fluids (e.g. the gas that is in stars or clouds in the interstellar medium) a variety of other systems are amenable to a fluid dynamical description - including the dust that makes up the rings of Saturn and even the orbits of stars in the galactic potential. Although some of the techniques of conventional (terrestrial) fluid dynamics are relevant to astrophysical fluids, there are some important differences: astronomical objects are often self-gravitating or else may be accelerated by powerful gravitational fields to highly supersonic velocities. In the latter case, the flows are highly compressible and strong shock fronts are often observed (for example, the spiral shocks that are so prominent in the gas of galaxies like the Milky Way).

In this course, we consider a wide range of topical issues in astronomy, such as the propagation of supernova shock waves through the interstellar medium, the internal structure of stars and the variety of instabilities that affect interstellar/intergalactic gas. These include, perhaps most importantly, the Jeans instability whose action is responsible for the formation of every star and galaxy in the Universe. We also deal with exotic astronomical environments, such as white dwarfs and neutron stars (supported by electron and neutron degeneracy pressure respectively) as well as the orbiting discs of gas and dust which feed black holes.

On completion of the module students should:  understand and learn to manipulate fluid dynamical equations in both Eulerian and Lagrangian form;  be able to set up and solve simple hydrostatic equilibrium situations in spherical and disc geometries;  be able to perform simple linear stability analyses and apply to wave propagation in hydrodynamical and magnetohydrodynamical systems;  apply Bernoulli's theorem to astrophysical applications;  understand the concept of shocks and their application to astrophysical blast waves;  understand the role of viscosity in accretion discs.

Introduction. The concept of a fluid, density and velocity. Kinematics: steady and unsteady flows, streamlines and particle paths; conservation of mass. Derivative following the fluid motion.

Dynamics. Pressure. (Inviscid) momentum equation for a fluid under gravity, application to force of jet on a wall, momentum equation in conservative form, role of ρuiuk, Poisson's equation for the gravitational potential and its derivation. The Virial Theorem.

Simple steady states. Simple (barotropic) relation between pressure and density, physical examples. Hydrostatic atmosphere under uniform gravity; self-gravitating isothermal slab and its relevance to galactic discs; self-gravitating polytropes as simple models of stars, mass-radius relation.

Energy. (entropy) equation with simple cooling law.

Sound waves. Sound speed (adiabatic and isothermal). Description of why shocks occur. Rankine-Hugoniot conditions. 1-D shock tube, application to blast waves and supernova remnants.

Bernoulli's equation and its applicability. De Laval nozzle and its relevance to astrophysical jets, Bondi accretion, stellar winds and mass loss.

Part II Physics – Options Courses 55 Fluid instabilities. Rayleigh-Taylor instability, Schwarzschild criterion; Thermal instability, Field criterion; statement of Kelvin-Helmholtz instability, Jeans instability.

Viscous flows. Linear and circular shear flows. Accretion discs.

Magnetohydrodynamics. The ideal MHD equations ( E +v^B = 0). Alfven waves.

BOOKS

Elementary Fluid Dynamics, Acheson, D (Oxford University Press 1994) An Introduction to Fluid Dynamics, Batchelor, G K (CUP 1991) Principles of Astrophysical Fluid Dynamics, Clarke, C J & Carswell, R F (CUP 2007) Hydrodynamics, Lamb, H (CUP 6th edn 1932, reprinted 1993) Fluid Mechanics, Landau & Lifshitz, (Pergamon Press 1987) An informal introduction to theoretical Fluid Mechanics Lighthill, M J (Oxford University Press 1993)

56 Part II Physics – Options Courses PARTICLE AND NUCLEAR PHYSICS

D R Ward

This course assumes familiarity with many of the topics in the "Advanced Quantum Physics" course. At the end of the course, the students should be familiar with the following features of Nuclear Physics:

 the structure of nuclei, and simple nuclear models such as the liquid drop model and the shell model;  techniques in scattering theory which are relevant in nuclear physics -- partial waves, Born approximation and compound nucleus formation;  the main types of nuclear decays, and with models for calculating these and the associated selection rules;  the key features of nuclear fission and fusion and their applications;

and with the following aspects of Particle Physics:

 how forces arise from virtual particle exchange (in outline only);  the particle content and interactions of The Standard Model, together with an understanding of how to apply (spinless) Feynman Diagrams to make order-of-magnitude estimates for rates and signatures of allowed/disallowed Standard Model processes;  the types of evidence upon which the three key parts of The Standard Model (i.e. electromagnetic, strong and weak), are founded;  how to determine which hadron decays would or would not be consistent with the quark content of the Standard Model, with parity violation/conservation, with energy- momentum conservation, etc.

INTRODUCTION Matter and Forces: Matter and generations. Leptons, quarks, hadrons and nuclei. Forces and gauge bosons.

NUCLEAR PHYSICS Basic Nuclear Properties: Natural units. Stable nuclei. Binding energy. Nuclear mass (Semi- Empirical Mass Formula). Spin and parity. Reactions and cross-sections. Scattering in Quantum Mechanics. Form factors and nuclear size. Nuclear moments.

Scattering and the Nuclear Force: General features. The deuteron. Nucleon-nucleon scattering. Partial waves. Scattering Length. Resonances. Partial decay widths. Breit-Wigner cross- section.

Nuclear Structure: Magic numbers, the Nuclear Shell Model and its predictions, excited states of nuclei (vibrations and rotations).

Nuclear Decay: Particle decays. Radioactivity and dating.  decay.  decay, Fermi theory of  decay.  decay.

Nuclear Fission and Fusion: Nuclear fission. Reactors. Nuclear fusion. Nucleosynthesis. So- lar Neutrinos.

Part II Physics – Options Courses 57 PARTICLE PHYSICS The Standard Model: Relativistic Kinematics (Four-vectors, invariant mass, colliders and s). Summary of the Standard Model of particle physics. Theoretical framework. Klein-Gordon and Dirac equations. Antimatter. Interaction via particle exchange. Yukawa potential. Virtual particles. Feynman diagrams.

Electromagnetic Interaction: QED. Gauge invariance. Electromagnetic interaction vertices. Scattering in QED. Discovery of quarks. Drell-Yan process. Experimental tests of QED. Higher or- ders and running of .

Strong interaction: QCD. Strong interaction vertices. Gluons, colour and self-interactions, colour factors. QCD potential, confinement and jets. Jets. Running of the strong coupling. Scattering in QCD. Experimental evidence for gluons, colour, self-interactions and the running of s.

Quark Model of Hadrons: Hadron wavefunctions and parity. Light quark mesons and masses. Baryons, baryon masses and magnetic moments. Hadron decays. Discovery of the J/. Charmo- nium. Charmed Hadrons. Discovery of the . Bottomonium and bottom hadrons.

Weak Interaction: Bosons and self-interactions. Weak charged current (W boson). Parity violation. Weak charged current lepton vertices.  and  decay. Lepton universality. Weak charged current interactions of quarks. Cabibbo suppression and the CKM matrix. Weak charged current quark vertices

Electroweak Unification: Neutral currents (Z0 boson). Electroweak Unification and the Glashow-Weinberg-Salam Model. Weak neutral current vertices and couplings. Summary of Standard Model vertices and drawing Feynman diagrams. Precision tests of the Standard Model at the Large Electron Positron collider (LEP). The top quark. The Higgs mechanism and the Higgs boson.

The Standard Model and Beyond: Incompleteness of the Standard Model. Neutrino oscillations. Beyond the Standard Model - supersymmetry.

BOOKS

Particle physics books (Perkins is closest to the course; Thomson or Griffiths are good if you want to go beyond): Introduction to High Energy Physics, Perkins D H (4th edn CUP 2000). Particle Physics, Martin B R & Shaw G (3rd edn Wiley 2008). Introduction to Elementary Particles, Griffiths D J (2nd edn Wiley 2009). Modern Particle Physics, Thomson, M A (CUP 2013)

Nuclear physics books (Krane is closest to the course): Introductory Nuclear Physics, Krane K S (Wiley 1988). Basic Ideas and Concepts in Nuclear Physics, Heyde K (3rd edn CRC Press 2004). Fundamentals of Nuclear Physics, Jelley N (CUP 1990).

Introductory books that cover the whole course, (at a lower level generally): Nuclear and Particle Physics, Martin B R (2nd edn Wiley 2009). The Physics of Nuclei and Particles, Dunlap P A (Thomson Brooks/Cole 2003).

58 Part II Physics – Options Courses QUANTUM CONDENSED MATTER PHYSICS

F M Grosche

This course will focus on collective quantum phenomena in solids, namely how physical phenomena emerge from the interaction of large numbers of atoms.

Electrons and phonons: The free Fermi gas. Elementary excitations. Heat capacity of insulators and metals. Semiclassical approach to electron transport in electric and magnetic fields. Screening and Thomas-Fermi theory. Plasma oscillations. Optical conductivity of metals.

Structure and bonding in solids: The variety of condensed matter: ordered, partially ordered and disordered. Types of bonding. Description of periodic solids. Bonding and structure. X-ray diffraction and reciprocal space.

Electrons in periodic solids: Bloch’s theorem, Brillouin zones, band structure. Crystal momentum. Nearly localised electrons: tight binding method, 1D chain, polymers. Nearly free electrons: plane waves and band gaps. High magnetic field: quantum oscillations and quantum Hall effect. Band structures of real materials: insulators and metals, optical transitions, de Haas-van Alphen, photoemission, tunnelling spectroscopies.

Semiconductors and semiconductor devices: Crystal structure and bandstructure. Effec- tive mass. Thermal equilibrium of quasiparticles in an intrinsic semiconductor. Doped semiconductors. pn junctions. Heterostructures and quantum wells. Devices: LED, solar cell, semiconductor lasers, field effect transistor.

Instabilities: Charge density waves. Interactions in the electron gas. Condensates. The ‘standard model’ of condensed matter physics and how it may fail.

BOOKS

Band Theory and Electronic Properties of Solids, J. Singleton (OUP 2008) Solid State Physics, Ashcroft N W and Mermin N D, (Holt, Rinehart and Winston 1976) Introduction to Solid State Physics, Kittel C (7th edn Wiley 1996) Principles of the Theory of Solids, Ziman J M (CUP 1972)

Part II Physics – Options Courses 59 SOFT CONDENSED MATTER

E M Terentjev

Introduction: What is soft matter? Forces, energies and timescales.

Elements of fluid dynamics: Navier-Stokes equation; Reynolds number; Laminar and boundary layer flows; Stokes Law and drag; Hydrodynamic interaction between colloidal particles; Im- plications for living systems; How bacteria swim; Viscosity of a hard sphere suspension; Non- Newtonian behaviour; Idea of complex viscosity; Linear viscoelasticity; Simple phenomenological models.

Surface energy and interactions: Surface energy and tension; Cahn-Hilliard model of a liquid interface; Wetting: Young’s equation and contact angles; hydrophobicity and hydrophilicity; Elec- trolyte solutions: Debye-Huckel theory; Interactions between colloidal particles, DLVO potential.

Self assembly: Chemical potential of systems that aggregate; Aggregation equilibria; Aggrega- tion of amphiphilic molecules; Critical micelle concentration; Shape of micelles; Lipid bilayers; Nature of the cell membrane; Curvature elasticity; Fluctuations of membranes; Examples of self assembly: viruses and nanotechnology.

Polymers and biological macromolecules: Examples of polymers; Single-chain statistics, self-avoiding walks; Entropic forces and excluded volume; Wormlike chain and persistence length, DNA; Phase transitions: Flory Huggins free energy for solutions; Good, theta and poor solvent conditions; Osmotic pressure in dilute conditions; Scaling in semi-dilute solutions; Chain dynamics in the Rouse model; Rubber elasticity.

BOOKS

Fluid Dynamics for Physicists, Faber T.E (CUP 1995) Soft Condensed Matter, Jones R.A.L. (OUP 2002) Biological Physics, Nelson P. (Freeman 2003) Molecular Driving Forces, Dill K.A. and Bromberg S., (Garland 2003)

ADVANCED TEXTS

Statistical Thermodynamics of Surfaces, Interfaces and Membranes, Safran S.A. (Addison Wesley 1994) Applied Biophysics, Waigh, T.A. (Wiley 2007) Physical Biology of the Cell, Phillips, R. Et al, (Garland 2009) Molecular Biophysics, Daune M. (OUP 1999)

60 Part II Physics – Options Courses COMPUTATIONAL PHYSICS

J S Richer and D F Buscher

Summary

This compulsory course builds on the IB course ‘Introduction to Computing’, and aims to develop further the computational physics skills acquired in that course. It consists of eight lectures in the first four weeks of Lent term, and four 3-hour practical classes in the MCS (formally PWF) during weeks 4, 5, 6 and 7 of the Lent term. In the lectures, various computational techniques used in physics will be presented, as well as general advice on programming and creating good quality software. In the practical classes, students will solve a series of computational physics problems. As in the IB course, programs will be written in C++ running under a LINUX environment. More sophisticated techniques and problems will be addressed, using external numerical libraries to handle some of the detailed computations. The focus is on self-learning, and learning by doing: the lectures are important, but it is only in the practical classes that real skills are developed. Demonstrators will be on hand in the MCS (formally PWF) to assist with problems.

This course also covers the material required for students planning to offer an (optional) Comput- ing Project (see separate page for full description).

Assessment

The credit for this course is approximately equal to one fifth of a unit of further work. During each of the practical sessions, a computational physics problem is to be solved by writing, running and testing a piece of software. When complete and tested, students will upload their solutions for checking to a dedicated file space for marking. The expectation is that students will gain high marks if they complete the exercises satisfactorily.

Syllabus

The computational physics topics covered will include Representation of numbers; roundoff error. Solution of Ordinary Differential Equations (ODEs): Euler and Runge-Kutta schemes; accuracy and stability. Dealing with data: interpolation, extrapolation; Fourier Transform techniques, including the FFT; fitting models to data. Pseudo Random Numbers; Monte-Carlo techniques; Ising model. Linear algebra

Part II Physics – Computing Exercises 61 COMPUTATIONAL PHYSICS PROJECT

J S Richer and D F Buscher

A Computational Physics Project constitutes one unit of further work and may be offered, optionally, by all Part II Physics students. There are no lectures or practical classes, but the compulsory course in Computational Physics provides the essential background for this work. Students chose one of a range of problems to investigate independently, using MCS (formally PWF) facilities or other equivalent facilities if they prefer. They will analyse the problem, write and test computer program to investigate and solve it, then write up their work in a report. It is required that the programs will be written in C++ running under LINUX, as in the IB course. However, if a student wishes to use other supporting languages (e.g. Java, or a scripting language like Python), this may be acceptable given prior consent from the Head of Class.

Students may start their project work at any time in the Lent term. The deadline for submission of the project report is 4:00pm on the first Monday of Easter term (28th April 2014).

One copy of the report should be handed in to the Teaching Office (Room 212B, Bragg Build- ing) in person before the submission deadline. In order to preserve anonymity when your report is looked at by the Part II examiners, your name must not appear on the report itself, but only on the cover sheet which you will be given when you hand it in. You should ensure that your candidate number appears on the first page of the report, together with the title of the report.

In addition, you should also upload, by the same deadline, your report in PDF format to the electronic course pigeon holes on the Physics PWF, along with the source code, program ex- ecutable, and possibly other relevant files you have created for the project (e.g. Makefiles, large graphic files, videos, etc).

The form of solution expected, and of the write up, will be described in more detail in the handout which contains the suggested projects. It will be marked by one of the Heads of Class, acting as Assessor for the Examiners. After the examination, you will receive a copy of the mark sheet, which will provide feedback on your performance. The marks allocated by the Head of Class are subject to moderation and scaling by the examiners, so the mark you receive may not match the final mark for this piece of work in the College Markbook.

Candidates may be selected for viva voce examination after submission, as a matter of routine, and therefore a summons to a viva should not be taken to indicate that there is anything amiss. You will be asked some straightforward questions on your project work, and may be asked to elaborate on the extent of discussions you may have had with other students. So long as you can demonstrate that your write-ups are indeed your own, your answers will not alter your project grades.

62 Part II Physics – Further Work THEORETICAL PHYSICS 1 - CLASSICAL FIELD THEORY (TP1)

C Castelnovo and M P Hobson

The course covers theoretical aspects of the classical dynamics of particles and fields, with emphasis on topics relevant to the transition to quantum theory. This course is recommended only for students who have achieved a strong performance in Mathematics as well as Physics in Part IB, or an equivalent qualification. In particular, familiarity with variational principles, Euler-Lagrange equations, complex contour integration, Cauchy’s Theorem and transform methods will be assumed. Students who have not taken the Part IB Physics B course ‘Classical Dynamics’ should familiarise themselves with the ‘Introduction to Lagrangian Mechanics’ material.

Lagrangian and Hamiltonian mechanics: Generalised coordinates and constraints; the La- grangian and Lagrange's equations of motion; symmetry and conservation laws, canonical mo- menta, the Hamiltonian; principle of least action; velocity-dependent potential for electromagnetic forces, gauge invariance; Hamiltonian mechanics and Hamilton's equations; Liouville's theorem; Poisson brackets and the transition to quantum mechanics; relativistic dynamics of a charged particle.

Classical fields: Waves in one dimension, Lagrangian density, canonical momentum and Ham- iltonian density; multidimensional space, relativistic scalar field, Klein-Gordon equation; natural units; relativistic phase space, Fourier analysis of fields; complex scalar field, multicomponent fields; the electromagnetic field, field-strength tensor, electromagnetic Lagrangian and Hamilto- nian density, Maxwell's equations.

Symmetries and conservation laws: Noether's theorem, symmetries and conserved currents; global phase symmetry, conserved charge; gauge symmetry of electromagnetism; local phase and gauge symmetry; stress-energy tensor, angular momentum tensor; transition to quantum fields.

Broken symmetry: Self-interacting scalar field; spontaneously broken global phase symmetry, Goldstone's theorem; spontaneously broken local phase and gauge symmetry, Higgs mechanism.

Phase transitions and critical phenomena: Landau theory, first order vs. continuous phase transitions, correlation functions, scaling laws and universality in simple continuous field theories.

Propagators and causality: Schrödinger propagator, Fourier representation, causality; Kram- ers-Kronig relations for propagators and linear response functions; propagator for the Klein- Gordon equation, antiparticle interpretation.

BOOKS

The Feynman Lectures, Feynman R P et al. (Addison-Wesley 1963) Vol. 2. Perhaps read some at the start of TP1 and re-read at the end. Classical Mechanics, Kibble T W B and Berkshire F H (4th edn Longman 1996): A clear basic text with many examples and electromagnetism in SI units. Classical Mechanics, Goldstein H (2nd edn Addison-Wesley 1980): A classic text that does far more than is required for this course, but is clearly written and good for the parts that you need. Classical Theory of Gauge Fields, Rubakov V (Princeton 2002): The earlier parts are closest to this course, with much interesting more advanced material in later chapters. Course of Theoretical Physics, Landau L D & Lifshitz E M: Vol.1 Mechanics (3rd edn Oxford 1976- 94) is all classical Lagrangian dynamics, in a structured, consistent and very brief form; Vol.2 Classical Theory of Fields (4th edn Oxford 1975) contains electromagnetic and gravitational theory, and relativity. Many interesting worked examples.

Part II Physics – Further Work 63 Quantum and Statistical Field Theory, Le Bellac M, (Clarendon Press 1992): An excellent book on quantum and statistical field theory, especially applications of QFT to phase transitions and critical phenomena. The first few chapters are particularly relevant to this course.

64 Part II Physics – Further Work THEORETICAL PHYSICS 2 - TOPICS IN QUANTUM THEORY (TP2)

A Lamacraft and M C Payne

The development of quantum theory during the 20th century leads to the introduction of completely new concepts to physics. At the same time, physicists were forced - sometimes unwillingly - to adopt myriad new techniques and mathematical ideas. In this course, we'll survey some of these more advanced topics.

This course is recommended only for students who have achieved a strong performance in Mathematics as well as Physics in Part IB, or an equivalent qualification. You should be VERY comfortable with the material from the Advanced Quantum Physics course. Some familiarity with Lagrangian mechanics (as discussed in TP1) is also useful but not essential.

The adiabatic approximation and Berry’s phase: A spin in a field. The adiabatic approximation. Berry’s phase.

Introduction to path integrals: The propagator. How does the Lagrangian appear in quantum mechanics? The method of stationary phase and the semiclassical limit.

Scattering Theory: Scattering in one dimension. Scattering amplitude and cross section. Opti- cal theorem. Green's function and relation to propagator. Born series and Born approximation. Partial wave analysis. Bound states.

Density Operators: Two kinds of probability. The density matrix and its properties. Time dependence of the density operator. Applications in statistical mechanics.

Identical Particles in Quantum Mechanics: Second quantisation for bosons and fermions. Density matrices for identical particles. Interference of condensates. Hanbury Brown and Twiss effect.

Lie Groups: Rotation group, SO(3) and SU(2). How Pauli solved the Hydrogen atom without the Schrödinger equation.

Relativistic Quantum Physics: Klein-Gordon equation. Lorentz group. Spinors and the Dirac equation.

BOOKS

Principles of Quantum Mechanics, Shanker R (2nd edn Springer 1994) Modern Quantum Mechanics, Sakurai J J (2nd edn Addison-Wesley 1994) Lectures on Quantum Mechanics, Baym G (Benjamin WA 1969)

For mathematical background we’d heartily recommend Mike Stone and Paul Goldbart’s Mathe- matics for Physicists: A guided tour for graduate students (SUP, 2009). This contains a lot of advanced material as well as much of what you covered in IB Mathematics.

A great resource for just about anything you may need to know about any of the functions we meet is the NIST Digital Library of Mathematical Functions at http://dlmf.nist.gov.

Part II Physics – Further Work 65 PART II EXPERIMENTS

D A Ritchie

There are 12 separate experiments, with varying numbers of places. Not all experiments will run in all six sessions – availability will depend in part on demand, and partly on the effort required to run them. The experiments are listed below.

([..] = maximum numbers of places available)

Waveguide [5] Dr Richard Saunders Part II Laboratory, Room 170 AP Waveguide propagation of a cm wavelength radio wave is investigated.

Phase-Locked Loops [6] Dr Andrew Irvine Part II Laboratory, Room 173 ME Operation and optimisation of phase-locked loops is investigated, for frequency locking and for recovery of signals buried in noise.

Optical Pumping of Rb [3] Dr Mete Atatüre Part II Laboratory, Room 168 AMOP The Zeeman effect in the ground state of the rubidium atom is studied, nuclear spins of 85Rb and 87Rb are obtained and multi-photon absorption and power broadening are investigated.

Semiconductor Quantum Devices [6] Prof. David Ritchie Part II Laboratory, Room 167 SP The resonant tunnelling of electrons in semiconductors is investigated at both room temperature and 77K.

Mobility [6] Prof. Henning Sirringhaus Part II Laboratory, Room 173 OE Propagation of carriers through a semiconductor is measured by a direct method.

Ferro-fluids [6] T.B.A. Part II Laboratory, Room 173 BSS An investigation is made of instabilities and pattern formations at Ferro-fluid interfaces.

Illuminance Fluctuation Spectroscopy [5] Dr Chris Edgcombe Part II Laboratory, Room 169 SMF The Boltzmann constant is obtained by studying the correlated fluctuations in scattering of laser light from polystyrene spheres dispersed in water.

Josephson [5] Dr Mike Sutherland Part II Laboratory, Room 186 QM The ratio of e/h is measured by studying the I-V characteristic of a Josephson junction immersed in liquid helium.

Particle Tracks [5] Dr Susan Haines Bragg, Room 178 HEP Properties of short-lived hyperons are measured by analysing photographs from a liquid hydrogen bubble chamber.

Scanning Tunnelling Microscopy [4] Dr Andrew Jardine Part IB Laboratory, Room 152 SMF The growth kinetics of graphite oxidation pits are investigated on atomic length scales.

66 Part II Physics – Further Work Pulsed NMR at 15 MHz [10] Dr Sarah Bohndiek Part II Laboratory Room 170 BSS This experiment investigates and demonstrates the principles of Nuclear Magnetic Resonance (NMR). Spin-echo methods are employed to study the characteristic NMR properties of a number of samples.

Submission of your report

One copy of your report should be handed in to the Teaching Office (Room 212B, Bragg Build- ing) in person before the submission deadline. In order to preserve anonymity when your report is looked at by the Part II examiners, your name must not appear on the report itself, but only on the cover sheet which you will be given when you hand it in. You should ensure that your candidate number, if known, appears on the first page of the report, together with the name of the experiment and the name of your Head of Class.

Before the end of the relevant term, the report will be assessed by the Head of Class, who will then conduct a viva voce examination (typically 30 minutes long). The student will be asked to give a short verbal summary (typically 10 minutes), normally uninterrupted, of the report during the examination. Students should expect to be contacted by the Head of Class shortly after the submission of their report, to arrange the examination.

These Head of Class will write a report to the Part II Examiners and will recommend a mark. These marks are not necessarily final and may be amended by the examiners, who will also look at the report and the Head of Class’s written assessments. After the viva, you will receive a copy of the mark sheet, which will provide feedback on your performance. The marks allocated by the Head of Class are subject to moderation and scaling by the examiners, so the mark you receive may not match the final mark for this piece of work in the College Mark- book. The following guidelines for allocation of marks to Part II experimental reports will be given to the Head of Class.  Understanding: (30%): of the physical system being measured, and of the experimental design.  The experiment (40%): how well the work was done, quality of results, discussion of errors.  Communications skills 1 - Report (20%): Was the report well written and clearly organised, with clear and well balanced arguments, appropriate use of figures, tables and references.  Communications skills 2 - Viva (10%): Was the student able to summarise the work and respond coherently to questions?

After the viva, the Head of Class will send the report and recommended mark to the Teaching Of- fice. After publication of the Part II Class List, students may, if they wish, retrieve their report from the Teaching Office.

If there are any queries concerning these arrangements, contact, Helen Marshall in the Teaching Office ([email protected]).

Part II Physics – Further Work 67 Contact details

Staff member Telephone Room Group E-mail (secretary) Atatüre, Dr M 66465(66298) 982 AMOP [email protected] Bohndiek, Dr S T.B.A. T.B.A. BSS [email protected] Edgcombe, Dr C 37335 443 PCS [email protected] Haines, Dr S C 37231 959 HEP [email protected] Irvine, Dr A C 37555 M232 ME [email protected] Jardine, Dr A P 37279(37336) 417 PCS [email protected] Ritchie, Prof. D A 37331/37255 361 SP [email protected] Saunders, Dr R D E 37301 F09 AP [email protected] Sirringhaus, Prof. H 37557 M208 OE/ME [email protected] Sutherland, Dr M 37389 463 QM [email protected]

68 Part II Physics – Further Work RESEARCH REVIEWS

F M Grosche

A research review is aimed at producing a descriptive and critical review of an area of physics of particular interest to the student. Its precise form may vary, and is to be agreed with the supervisor. The topic could range from a review of the very latest research in a particular area to, for example, a classic discovery of the twentieth century. In some cases the supervisor may indicate one or two articles which serve as an introduction; in other cases the student may need to search in computerised databases or citation indices to find relevant papers.

The research review abstracts are available on the web: see (www.teach.phy.cam.ac.uk/pt2reviews/) for a direct link to the research review page). Stu- dents may also suggest reviews of their own, but they must have a supervisor (who may be external) and the review must be approved in advance. Students interested in a particular review should discuss it as soon as possible with the relevant supervisor. The list of reviews on the web will be continuously updated as new ones are added.

By Friday 25th October 2013, students should select (via a form on the Web) the review topics they would like to do, in order of preference. A ballot will then be held in order to assign titles to students in a fair way, and students and supervisors informed of the outcome.

Reviews can be started during the Michaelmas term or they may be deferred until the Lent term. It might be a good idea to start some reading over the Christmas vacation. It is important to re- member that the review counts for only about half a Tripos paper, so students should bear this in mind when deciding how much time to devote to it. During the preparation for the writing of the report, students will be asked to give a short talk presenting their preliminary work to a group of students writing research reviews in similar areas. It is expected that supervisors will organise these group sessions, which will consist of, say, four to eight students, in the last two or three weeks of the Lent term. Students will receive feedback on the content and presentation of their reviews from the supervisors present and from their fellow students. This form of presentation is aimed at developing communication and presentational skills. You will be awarded 5% of the available marks for the Research Review upon giving the presentation (irrespective of its quality).

The Web of Science database (http://wos.mimas.ac.uk) may be used to find relevant papers. Stu- dents must first sign a form (available from the Rayleigh Library) unless they signed one last year.

The write-up of the review will typically be in the style of a paper published in a scientific journal. The style of the review should be agreed with the supervisor. The review should describe and explain the main features of the subject, suggesting in which direction the field is moving, and drawing some conclusions. The main text should be concise (3000 words maximum, including any appendices). In addition, there must be an abstract of not more than 250 words. The student and supervisor should discuss the general structure of the review before writing is started, but the supervisor should not read a full version of the text until it is submitted. A set of handy tips and information is given in the booklet entitled Keeping Laboratory Notes and Writing Formal Reports, which is handed out to students at the start of the year - make sure you get one.

The deadline for submission of the research review is 4:00 pm on the first Monday of Easter Full Term (28th April 2014). Two copies of the review should be handed in to the Teaching Office (Room 212B, Bragg Building) in person before the submission deadline. In order to preserve anonymity when your review is looked at by the Part II examiners, your name must not appear on the review itself, but only on the cover sheet which you will be given when you hand it in. You should ensure that your candidate number appears on the first page of the research review, together with the title of the review and your supervisor’s name.

Part II Physics – Further Work 69 As soon as possible after submission, the review will be assessed by two people, normally the supervisor and another staff member, who will conduct an informal oral examination (typically 30 minutes long) of the student on the work. The student will be asked to give a short verbal summary, normally uninterrupted, of the review during the interview. The assessor, who will be appointed by the Teaching Committee, will generally not be a specialist in the field. Students should expect to be contacted by their supervisor shortly after handing their review in, to arrange the oral examination.

These assessors will write a report to the Part II Examiners and will recommend a mark. These marks are not necessarily final and may be amended by the examiners, who also look at the reviews. After the viva, you will receive a copy of the mark sheet, which will provide feedback on your performance. The marks allocated by the assessors are subject to moderation and scaling by the examiners, so the mark you receive may not match the final mark for this piece of work in the College Markbook.

The following guidelines for allocation of marks to Part II Research Reviews will be given to assessors. Each heading carries equal weight.

 Scientific content: How much appropriate understanding of science (particularly physics) was shown?  Quality of work: How carefully/accurately/successfully was the work planned and performed? Was an appropriate amount of relevant material included?  Communication skills: Report: was the report well written and clearly organised, with clear and well-balanced arguments, appropriate use of figures and tables, etc? Viva: was the student able to summarise the work and to respond coherently to questions?

After the oral examination, the assessors will send the report and recommended mark to Dr Malte Grosche, (Room 501, Mott Building) and will return the review to the Teaching Office (Room 212B, Bragg Building). After publication of the Part II Class List, students may, if they wish, retrieve one copy of their review from the Teaching Office.

If there are any queries concerning these arrangements, contact Dr Malte Grosche, (Room 501, Mott Building, telephone 37392, e-mail: [email protected]).

70 Part II Physics – Further Work PHYSICS EDUCATION

L Jardine-Wright

Physics Education represents one unit of Further Work. It is aimed at those students considering a career in Physics Education, and offers experience of developing and presenting teaching material at the secondary-school level. This course aims to provide practical experience for the development of a wide range of transferable skills including: planning and organisation; time- management; communication and negotiation.

The course will typically be based on planning and preparing for, and successfully completing, a ½ day per week placement at a local school during the Lent Term, including developing and de- livering a Special Project, under the supervision of a teacher. The student and their Supervising Teacher will collaborate to identify the basis of the Special Project. The Special Project must support physics education in the placement school and be approved by the Supervising Teacher.

All those interested in undertaking this course must attend a Preliminary Meeting, which will be held at the Cavendish Laboratory between 2-5pm on Wednesday 9th October 2013, in the Bragg Committee Room (room 213) and pass a background check conducted by the Criminal Records Bureau. Access to places on this course is limited and candidates will be selected by interview and reference from their Director of Studies. Interviews will take place on Friday 11th Oc- tober 2013 in the Department Administrator’s office (room 207) and students will be asked to sign up for times at the preliminary meeting on the 9th. Interviews will be 15 minutes long and may require a short period to be missed from lectures on that day.

Placements will be identified for each student by the end of November 2012. It will be the responsibility of the student to contact their Supervising Teacher to arrange an appropriate date and time to begin their placement, and to make appropriate arrangements to complete a placement to- talling 30 hours contact time. All placements must begin before the end of the first week of the Lent Term, and be completed before the end of Lent Term.

Students must write a written report about their work. The written report should be concise (2000 words maximum, excluding any appendices) on some area of Physics Education, approved in advance by the Head of Class. The student should discuss the general structure of the report with their Supervising Teacher, and the Head of Class, before writing is started, but the Head of Class should not read a full version of the text until it is submitted. During the preparation for the writing of the report, students will be asked to give a short talk presenting their preliminary work to the Head of Class and a group of students writing similar reports. It is expected that the Head of Class will organise the group session in the last two or three weeks of the Lent term. Students will receive feedback on the content and presentation of their reports from those present. This form of presentation is aimed at developing communication and presentational skills. You will be awarded 5% of the available marks for the written report upon giving the presentation (irrespective of its quality).

Assessment will be based on:  The candidate’s class presentation (5 %);  A written assessment of performance from the Supervisory Teacher (5%)  The candidate’s project delivery, written report and viva-voce examination with the Head of Class and an Assessor (90 %). The written assessment of performance by the Supervisory Teacher is considered confidential to the Head of Class, and will therefore be sent directly to the Head of Class by the Supervising Teacher: it will not be seen by the student.

The deadline for submission of the written report is 4:00pm on the first Monday of Easter Full Term (28th April 2014).

Part II Physics – Further Work 71

Two copies of the report should be handed in to the Teaching Office (Room 212B, Bragg Building) in person before the submission deadline. In order to preserve anonymity when your report is looked at by the Part II examiners, your name must not appear on the report itself, but only on the cover sheet which you will be given when you hand it in. You should ensure that your candidate number appears on the first page of the report, together with the title of the report, the name of the Head of Class, and the name of your Supervis- ing Teacher.

As soon as possible after submission, the report will be assessed by two people, normally the Head of Class and another staff member, who will then conduct the viva voce examination (typically 30 minutes long) to be given by the student. The student will be asked to give a short verbal summary (typically 10 minutes), normally uninterrupted, of the report during the examination. The assessor, who will be appointed by the Teaching Committee, will generally not be a specialist in the field. Students should expect to be contacted by the Head of Class shortly after the submission of their report, to arrange the examination. These assessors will also be given a copy of the Supervis- ing Teacher’s written assessment.

These assessors will write a report to the Part II Examiners and will recommend a mark. These marks are not necessarily final and may be amended by the examiners, who will also look at the reports and the Supervising Teachers’ written assessments. After the viva, you will receive a copy of the mark sheet, which will provide feedback on your performance. The marks allocated by the assessors are subject to moderation and scaling by the examiners, so the mark you receive may not match the final mark for this piece of work in the College Mark- book.

The following guidelines for allocation of marks to Part II Physics Education reports will be given to assessors.  Quality of work (60%): How carefully and accurately was the work planned and performed? Was an appropriate amount of relevant material included?  Communications skills 1 - Report (20%): Was the report well written and clearly organised, with clear and well balanced arguments, appropriate use of figures, tables and references.  Communications skills 2 - Viva (10%): Was the student able to summarise the work and respond coherently to questions?

After the formal presentation, the assessors will send their report and recommended mark to the Head of Class and will return the student’s report to the Teaching Office. After publication of the Part II Class List, students may, if they wish, retrieve one copy of their report from the Teaching Office.

If there are any queries concerning these arrangements, contact, Dr L Jardine-Wright (Room 212A, Bragg Building, telephone 33318, email [email protected]).

72 Part II Physics – Further Work CONCEPTS IN PHYSICS

R Needs

This course is not examinable, but the material covered overlaps with and illustrates many aspects of the Part II syllabus. It aims to consolidate core physics and provide revision of a number of key topics from a somewhat different perspective to that presented in the core course. The aim is to provide additional background to a number of major themes of physics, to sketch the connections between them and to investigate unresolved questions. Attendance is strongly advised for all Part II students. The lectures are likely to cover at least some of the following:

Scaling Laws in Physics and Elsewhere: Dimensional analysis and the Buckingham  theorem, general pendulum, explosions, drag in fluids, flow past a sphere, Kolmogorov spectrum of turbulence, law of corresponding states.

Chaos: Discovery of chaotic behaviour. Necessary conditions for chaos. Damped driven nonlinear pendulum, phase space diagrams, Poincare sections, bifurcation diagrams, Lorenz attrac- tor. Logistic map, limit cycles, period doubling, Hyperion.

More on non-linear behaviour: Self-organised criticality, examples of scaling laws, fractals, sand piles.

Order, broken symmetry and phase transitions: the development of long-range order as a broken symmetry; why phase transitions are abrupt; scaling laws and critical phenomena.

The Galileo Case: Ptolemy, Copernicus, Tycho Brahe, Kepler and the Galilean revolution. The origins of experimental science, Galileo’s physics, what Galileo got right and what he got wrong. The trial of Galileo. Physics as a hypothetical-deductive system. Galilean relativity, the Newtonian revolution.

Thermodynamics and Statistical Mechanics: The nature of heat, caloric theories, real steam engines and the genius of Carnot, caloric as entropy, the statistical nature of the Second Law, the origin of irreversibility.

Atoms get real - the kinetic theory: Tracing the history of atoms from Boyle to the 19th century.

The Origin of Quantum Mechanics: The discovery of quanta. Classical derivation of the Stefan-Boltzmann law. Planck's (non)-statistical mechanics, how Einstein discovered photons.

The Origin of Maxwell’s Equations: Origins of electromagnetism, Maxwell and analogy in physics, vortices and magnetic fields, a physical model for the aether, the origin of the displacement current, a paper which is ‘great guns’ - light as electromagnetic waves. Hertz and the properties of electromagnetic waves. The discovery of the photoelectric effect.

Relativity: The real story of the discovery of the Special Theory of Relativity, the difficult route to the General Theory, Mach’s principle, tests of General Relativity, unresolved issues

Physics of the Cosmos: The technology of cosmology. Application of laboratory physics to the Universe on the largest scales: its successes, the origin of the Cosmic Microwave Background Ra- diation.

Part II Physics – Non-examinable courses 73 BOOKS

The following books may be useful as background reading to help your understanding: Theoretical Concepts in Physics, Longair M S (2nd edn 2003) The New Physics, Davies P C W (CUP 1989) The Galileo Affair, Finocchiaro M A (U Calif Press 1989) Inward Bound: Of Matter and Forces in the Physical World, Pais A (OUP 1986) Subtle is the Lord. The Science and Life of Albert Einstein, Pais A (OUP 1982) Scaling, Self-similarity, and Intermediate Asymptotics, Barenblatt G I (CUP 1996) Does God Play Dice? Stewart I (2nd edn Penguin 1997) Chaos: Making a New Science, Gleick J (Viking NY 1987) Chaotic Dynamics - an Introduction, Baker G L and Gollub J P (CUP 1990)

74 Part II Physics – Non-examinable courses Part III Physics

Comments may be sent to [email protected] Enquiries/queries: [email protected]

choices as the year proceeds which allow you, for 7.1 INTRODUCTION instance, to select a bias towards particular broad areas of physics such as condensed matter phys- The four-year course, of which Part III is the final ics, particle physics, astrophysics, or semiconduc- component, is designed for students who wish to tor physics. You can also range over the spectrum pursue a professional career in physics, in aca- from strongly experimental to highly theoretical demic or industrial research. It leads to an hon- physics, and choose from a range of specialist op- ours degree of Master of Natural Sciences, M.Sci., tions. together with a B.A., though the latter cannot be All students undertake a substantial research pro- conferred until the end of the fourth year. ject, the equivalent of about six weeks of full-time Part III Physics is a demanding course, and work. courses assume an upper second class level of un- The Michaelmas Term lectures are the Major Top- derstanding of the core and relevant optional ma- ics, which cover substantial areas of physics. You terial in Part II Physics. Candidates for the are examined in three or more of them at the start four-year course must achieve at least a 2:1 of the Lent Term. in Part II Physics, (or have received from the The Lent Term lectures are the Minor Topics, Faculty Board a dispensation from this condition). which cover more specialised areas, mostly of ac- Admission to Part III Physics is also available to tive research interest in Cambridge. You are ex- those who have obtained a First Class in Half Sub- amined in three or more of them at the start of the ject Physics in Part II Physical Sciences. Easter Term. The qualification requirement for students who We do not expect any student to take more than have studied other Part II tripos e.g. Part II As- the minimum number of units of work in any trophysics or Part II Mathematics will be pub- category. The great majority of students will find lished in the Reporter. the workload demanding even at this level. We You must have made financial provision by se- recognise, however, that students may have good curing a four-year grant from your LEA or reasons for wishing to take additional courses for equivalent funding body during your second credit. Marks for all examination papers en- year. If you have any doubt about this, you tered will appear on the students’ Univer- should see your college Tutor or Director of sity transcripts. Within any part of the Studies without delay. examination (Major Topics, Minor Topics) the best results meeting the minimum re- 7.2 MASTER OF ADVANCED STUD- quirement will count towards the class for IES (MASt) IN PHYSICS the year. You are of course free to attend as This is a taught postgraduate course, which con- many lecture courses as you wish, without neces- sists of the same content as Part III Physics. The sarily offering them for examination. course is designed for students who hold a 3-year Some of the Major and Minor Topics are given by undergraduate degree who wish to pursue a re- staff from other Departments such as the Institute search degree. The entry requirement for the of Astronomy and the Department of Earth Sci- MASt is a qualification comparable to an upper ences. You can also take as Major or Minor Topics second class or better Bachelor’s degree in Phys- certain courses given in Part III of the Mathemati- ics. cal Tripos but you should note that the style of the Part III Mathematical Tripos Options and Exami- 7.3 OUTLINE OF THE COURSE nation is different from that experienced in the The course aims to bring you close to the bounda- Part III Physics Options, reflecting the difference ries of current research, and is therefore some- in approaches of the two Departments. what linked to the expertise from within the The possibility exists of undertaking a vacation specific research groups. You make a series of project during the previous Long Vacation or the

Part III Physics 75 optional course on Entrepreneurship during the assessed by two staff members after an oral ex- Lent Term, for credit in the Tripos by replacing a amination. Minor Topic in each case. 7.4.2 Major Topics Ability in general physics is fostered by examples classes in the Easter Term and examined by a The seven options given during the Michaelmas general paper at the end of the Easter Term. Term cover major areas, and in each, physics is presented as a connected discipline drawing upon 7.4 DETAILS OF THE COURSES the material of the first three years to take the topic close to the frontiers of current research. Students will be e-mailed to register via Candidates choose three or more Major Topics for http://www.phy.cam.ac.uk/teaching/ before the examination. The courses (of 24 lectures) are: start of Michaelmas Term. The course will begin with a meeting on the first Wednesday of Full Advanced Quantum Condensed Matter Term (9th October 2013) at 12.30pm in the Physics Small Lecture Theatre at the Cavendish Soft Matter and Biological Physics Laboratory. Relativistic Astrophysics and Cosmology Particle Physics 7.4.1 Project work Physics of the Earth as a Planet Please note that from 2014-15 the project Quantum Condensed Matter Field Theory allocation procedure with be changing. Atomic and Optical Physics

All students must undertake a project which is All of the courses above are examined at the start worth a third of the years’ marks. A list of projects of the Lent Term. will be provided by the beginning of the Michael- Students who are especially strong in mas Term. Many of these will be supervised by Mathematics may wish to replace one of the members of the Physics Department, but mem- Topics above with an approved course, also of 24 bers of other Departments will also be involved. lectures, taken from Part III of the Mathematics The projects can be experimental, theoretical, Tripos. The course available in Part III Mathemat- computational, observational, or some suitable ics in the coming year is: combination of these. There will be scope for ini- Quantum Field Theory tiative and originality in carrying out a project, and it should form a valuable preparation for a re- Students taking this course take the same paper as search career. the Part III Mathematics students, in June. Project work will take place mainly in the Lent Term. Weeks are set aside for finishing up pro- 7.4.3 Minor Topics jects at the beginning of the Easter Term. You choose for examination three or more of the Communication skills are essential if you are to Lent Term Minor Option courses from about have a successful career in science. Toward the twelve (although you may substitute other courses end of Lent term a meeting will be arranged in for these: see below). They are more specialised which you will have the chance to give a fifteen than the Major Topics and most build upon the minute oral presentation on your project to other material presented in the Michaelmas Term. students working in similar areas and their super- Some of them assume specific knowledge of par- visors. This presentation counts for 5% of the ticular Major Topics – the syllabuses make clear available marks for the project (irrespective of the which. The Minor Topics are: quality of your presentation). You should note (i) Theoretically biased: that about one-third of the total marks for the project will be based on an assessment of the Gauge Field Theory quality of your written report and your ability to Quantum Information explain and defend your work in the viva. (ii) Condensed-Matter Physics: Bench work on experimental projects should be substantially complete by the end of the Lent Superconductivity and Quantum Coherence Term. You must submit your project report by the third Monday of the Easter Term, and it will be (iii) Astrophysics and Particle Physics

76 Part III Physics The Frontiers of Observational Astrophysics 7.4.6 Long-Vacation Projects Particle Astrophysics The Formation of Structure in the Universe Scientific work during the Long Vacation prior to your fourth year can count as project work which (iv) Other: may replace a Minor Option. The full details can be obtained from Dr Padman ([email protected], Atmospheric Physics Astrophysics Group), but you must get your pro- Medical Physics posal approved in advance, before the end of the Biological Physics preceding Easter Term. Forms are available from Non-linear Optics and Quantum States of the Teaching Office. You will be required to name Light in advance a suitably qualified on-site supervisor 7.4.4 Other Lent Term courses who is willing to write retrospectively to Dr Pad- man describing the work you have done and giv- You may also take any of the courses below: each ing an assessment of your effectiveness. Normally may be substituted for one Minor Topic. the programme must be of at least two months duration and must include a substantial element (i) Interdisciplinary Courses: of independent or original work. It is important Materials, Electronics and Renewable Energy that the project includes a significant amount of (taught by Physics) physics and is not, for example, simply a series of Climate Change routine measurements or entirely devoted to (Department of Earth Sciences) computer programming. Atmospheric Chemistry and Global Change Vacation projects within the University may be of- (Department of Chemistry) fered through the Undergraduate Research Op-

portunities Programme (UROP). See (ii) Shared Course with Engineering http://www.phy.cam.ac.uk/teaching/UROPS/uro

p.php for details. Some of these projects may be Nuclear Power Engineering suitable as assessed Long-Vacation Work. The

teaching web pages All of these courses except for "Materials, Elec- http://www- tronics and Renewable Energy" are taught by de- teach.phy.cam.ac.uk/teaching/vacWork.php partments other then Physics. They are examined might offer some useful suggestions. in separate papers – the Interdisciplinary Courses at the end of the Easter Term and Nuclear Power 7.4.7 Entrepreneurship Engineering with the Part IIB Engineers at the start of Easter Term. The synopsis for the Entrepreneurship course is given later. The course will be lectured together (iii) The 24 lecture Part III Mathematics course with the Minor Topics, but will be assessed by the Advanced Quantum Field Theory completion of assignments as described in the synopsis. may be substituted for one of the Minor Topics. This course is only suitable for students 7.4.8 Examples Class in General Phys- whose mathematics is particularly strong ics and will also be examined towards the end of the Easter Term. The Part III course is designed to build upon the physics covered in the first three years and will 7.4.5 Further Work take many subjects to the frontiers of current un- One or two units of Further Work may be substi- derstanding. However, it is important that core tuted for Minor Topics. The two types of Further physics is reinforced at the same time, and the examples classes, which run during the Easter Term Work available in 2013-14 are: are designed to help with this. They will focus on (i) A Long Vacation Project the key topics covered in the core Physics courses (ii) A course in Entrepreneurship and may include introductory summary talks and examples sheets modelled upon short questions These are described in the following sections. and more general problems. The June 2003 - 2013 General Papers indicate the type of question which will be set. They will be designed to empha-

Part III Physics 77 sise the straightforward application of core phys- 7.8 THE EXAMINATION ics to reasonable problems, and be an appropriate The Major Topics and the Project each contribute preparation for the three-hour examination in approximately one-third of the total marks. The general physics which forms part of the final as- Minor Topics and General Physics Paper each sessment. contribute approximately one-sixth of the total 7.5 RESTRICTIONS ON COMBINA- marks. TION OF COURSES The marks all courses will appear on the Univer- sity transcript, with the best marks for the mini- While every effort is made to arrange the timeta- mum requirement being used to establish the final ble, it is inevitable that some combinations of class for the Examination. courses will be ruled out by their schedule. 7.8.1 Examiners’ Notices 7.6 SUPERVISIONS Specific information about the examination is We do not offer formal supervisions in Part III. given in notices put up on the Part III notice Lecturers are expected to provide some form of board outside the Pippard Lecture Theatre. You learning support, but the form it takes is up to the should make sure that you read these regularly. individual lecturer. It is likely to take the form either of examples classes, with or without demon- 7.8.2 Examination Entries strators (depending on the number of students) or of large-group supervisions or seminars. Examination entries are made through the Cam- SIS on-line system, and should be completed in A consequence of this is that, neither students nor consultation with your Director of Studies. The lecturers need wait before arranging sessions. The deadline is usually about the middle of November. lecturer may choose to announce arrangements You will have a further chance during Lent Term during the first lecture, or may announce them to modify your entry for the Minor Topics papers. through the class email list. These procedures are largely outside of the De- The class email list depends on each student sign- partment’s control, and are continually evolving. ing up for the particular course. You will be re- We will provide further information about proce- minded about the sign-up before the start of each dures for examination entries as it becomes avail- of Michaelmas and Lent Terms. If you decide to able. change options during the Term, you should make 7.8.3 The Written Papers for Part III the necessary change on the teaching website, and also notify the relevant lecturers directly. Major Topic Papers: 7.7 NON-EXAMINED WORK These are taken at the beginning of the Lent Term (2 hours each). In the Lent Term there are two non-examinable courses, one on Philosophy of Physics and one on Ethics of Physics. Minor Topic Papers: These are taken at the beginning of the Easter To advertise research opportunities at the Caven- Term (1.5 hours each). dish various open days will be held which cover the activities of the major groups in the laboratory. Dates are will be posted on the Part II and General Physics Paper: Part III notice boards. This is taken towards the end of the Easter Part III students are also welcome at the large Term (3 hours). number of Research Seminars and other lectures in the Department, particularly those organised QFT/AQFT: by the Cavendish Physical Society lectures at Those students who have substituted these 4.00pm on some Wednesdays. These are adver- Part III Mathematics courses for Major or tised on notice boards, and summarised on the Minor Topics will take the same examination Cavendish web page. as the Mathematics students, towards the end of the Easter Term.

Interdisciplinary courses:

78 Part III Physics Each of the interdisciplinary courses is treated as a Minor Topic. The three interdisciplinary courses will all be examined in separate papers during the main Examinations Period at the end of Easter Term.

Nuclear Power Engineering: Students taking these Topics will be examined with the Part IIB Engineers in one and a half- hour paper at the start of the Easter Term. A summary of the choices available is given below.

Part III Physics 79 Lectures Course Exams

Michaelmas Term

Major Topics 24 Advanced Quantum Condensed Matter Physics 24 Atomic and Optical Physics 24 Particle Physics 2h paper for each 24 Physics of the Earth as a Planet option, Start of Choose 24 Quantum Condensed Matter Field Theory Lent 3 24 Relativistic Astrophysics and Cosmology 24 Soft Matter and Biological Physics from Part III Mathematics 24 Quantum Field Theory 3h paper, June

Lent Term Minor Topics 16 Atmospheric Physics 12 Biological Physics 16 Formation of Structure in the Universe 12 Frontiers of Observational Astrophysics 1.5h paper for each 12 Gauge Field Theory option, Start of 12 Medical Physics Easter 12 Non-linear Optics and Quantum States of Light 16 Particle Astrophysics 12 Quantum Information 12 Superconductivity and Quantum Coherence

Interdisciplinary Papers Choose 12 Atmospheric Chemistry and Global Change 1.5h paper for 3 12 Climate Change each, June 12 Materials, Electronics & Renewable Energy from Part III Mathematics 24 Advanced Quantum Field Theory 3h paper for each, June from Part IIB Engineering 12 Nuclear Power Engineering 1.5h paper, Start of Easter

Further Work Entrepreneurship Course work Report of Vacation Project Other requirements Research Project Course work  General Paper 3h paper, June 

80 Part III Physics 7.9 SOME IMPORTANT DATES Note: This list is not exhaustive, and may be superseded by announcements on the TIS

Tuesday 8th October 2013 Start of Michaelmas full term Wednesday 9th October 2013 12.30 General Registration (Small Lecture Theatre, Cavendish Laboratory) and buffet lunch outside the Pippard Lecture Theatre Wednesday 9th October 2013 Start choosing a project Monday 14th October 2013 16.00 Vacation work report deadline Wed 16th October 2013 14.00 Deadline for signing up for supervisions on Major Topics Thursday 24th October 2013 Supervisors can now make decisions on students for projects Friday 1st November 2013 Deadline for choosing a project (but don’t leave it this late!) Friday 6th December 2013 16.00 Deadline for first brief progress report on Project (summarising the goals of the project); hand in to the Teaching Office Friday 6th December 2013 End of Michaelmas full term Monday- 13th–15th January 2014 Examinations on Major Topics (check the TIS for Wed details) Tuesday 14th January 2014 Start of Lent full term Monday 3rd February 2014 14.00 Deadline for commitment to examination in the Entrepreneurship Course Monday- 3rd -14th March 2014 Presentations of projects (will be organised by your super- Friday visor). Some supervisors prefer to do these early in Easter Term. Wed 5th March 2014 16.00 Deadline for second brief progress report on Pro- ject (outlining progress and confirming that you have adequate material to complete the project); hand in to the Teaching Office Friday 14th March 2014 End of Lent full term Tuesday 22nd April 2014 Start of Easter full term Tuesday- 22nd -25th April 2014 Examinations on Minor Topics (check the TIS for Friday details) Friday 25th April 2014 14.00 Examples Classes on General Physics begin (eight classes on Tuesdays and Fridays, 14:00-16:00) in the Pippard Lecture Theatre. Monday 12th May 2014 16.00 Deadline for handing in Project Work (two copies) 13th–23rd May 2014 Oral examinations on Projects (will be organised by your supervisor) Monday 2nd June 2014 Examination on General Physics (check the TIS for details) Friday 13th June 2014 End of Easter full term

Part III Physics 81 Late Submission of Work

In accordance with the University’s regulations, a Part III Project (which amounts to more than 10% of the total year’s mark) submitted after the advertised deadline will not count towards your final examination mark, unless the University’s Applications Committee grants an extension of time on the grounds that there are mitigating circumstances. Any application for such an extension should be made by your college Tutor to the Applications Committee.

For units of Further Work amounting to less than 10% of the total year’s mark, the Department may grant an extension of time on the grounds that there are mitigating circumstances. Any application for such an extension should be made by your college Tutor or Director of Studies to the Director of Undergraduate Teaching, c/o Teaching Office, Cavendish Laboratory, ([email protected]). In either case, you should submit the work as soon as possible after the deadline.

82 Part III Physics 7.10 LECTURE LIST

PART III PHYSICS

Departmental Contact: Helen Marshall: E-mail: mailto:[email protected] Course Website: http://www.phy.cam.ac.uk/teaching/

Students must offer three or more courses from Major Topics, together with three or more courses from Minor Topics. Quantum Field Theory may be substituted for one Major Topic. A Vacation project and courses from Interdisciplinary Topics, Advanced Quantum Field Theory, Nuclear Power Engineering and Further Work may each be substituted for one Minor Topic.

The courses from the Major Topics and Minor Topics and Nuclear Power Engineering, are examined at the start of the term following that in which they are given. Quantum Field Theory, and Advanced Quantum Field Theory and courses from the Interdisciplinary Topics will be examined in June. The Entrepreneurship course from Further Work is continually assessed.

All students are recommended to attend the Non-examinable courses.

The course will begin with a meeting on the first Wednesday of Full Term (9 Oct.) at 12.30 p.m. in the Small Lecture Theatre.

For the up-to-date lecture list please go to: http://www.phy.cam.ac.uk/teaching/lectures.php

Part III Physics 83 ADVANCED QUANTUM CONDENSED MATTER PHYSICS

C Barnes

It is expected that students will have taken the Part II option course Quantum Condensed Matter Physics. However, the course includes an introductory section that discusses and refreshes all solid state concepts needed. It is therefore possible to take the course without having taken Quan- tum Condensed Matter Physics.

Revision of key concepts of independent-electron framework (Part II)

Electron-electron interactions: The many-electron problem: Exchange and correlation effects; Hartree-Fock theory; Phase diagram of the electron gas. Density functional theory: Hohen- berg-Sham theorem, molecular dynamics. Linear response theory of the electron gas. Introduction to Fermi liquid theory. Strongly correlated electron systems.

Magnetism: Magnetic exchange, Heisenberg model, giant & colossal magnetoresistance.

Electron-photon interactions: Linear optical response: Kramers-Krönig relations; Optical properties of semiconductors. Excitons in 3D and low-dimensional systems. Bose-Einstein condensation in excitonic systems.

Electron-phonon interactions: Origin of electron-phonon coupling: Scattering, mass en- hancement, polarons. Effective electron-electron interaction through exchange of phonons.

Electrical transport: Classical transport: Boltzmann equation, AC conductivity of metals, Re- laxation time. Quantum transport: Conductance quantization; Coulomb blockade.

Superconductivity: Phenomenology; Microscopic BCS theory, High-Tc superconductivity.

BOOKS

Basic general: Solid State Physics, Ashcroft & Mermin (Holt, Rinehart and Winston, 1976) Introduction to Solid State Physics, Kittel (Wiley, 7th edition 1996) The Physics and Chemistry of Solids, Elliott (Wiley, 1998)

Advanced general: Solid State Physics, Grosso, Parravicini, (Academic Press, 2000) A quantum approach to Condensed Matter Physics, Taylor & Heinonen (Cambridge 2002) Principles of condensed matter physics, Chaikin &Lubensky (Cambridge 1995) Solid State Physics Phillips (Cambridge University Press 2012)

Specialized subjects: Quantum Theory of the Electron Liquid, Vignale (Cambridge 2005) Quantum Theory of Many-Particle Systems, Fetter & Walecka (Dover 2003) Magnetism in Condensed Matter, Blundell (Oxford 2001) Superconductivity, Superfluids and Condensates, Annett (Oxford 2004) Fundamentals of Semiconductors, Yu & Cardona (Springer, 1996) Optical Properties of Solids, Fox (Oxford 2005)

84 Part III Physics – Major Topics ATOMIC AND OPTICAL PHYSICS

Z Hadzibabic

The ability to cool and control atoms by laser light has given a completely new twist to the traditional field of atomic physics in recent years. The Nobel prizes in physics of 1997, 2001, and 2005 document the fascinating recent advances in this field. Macroscopic quantum phenomena such as Bose-Einstein condensation have become experimentally accessible and the fundamental laws of quantum mechanics have been studied in new ways and with unprecedented precision. This course will serve as an introduction to this exciting field and give insight into the current state of research. It is intended to provide the basic understanding needed for the current research on a wide range of topics involving atoms, lasers, and quantum gases. Emphasis will be put on the connection between theory and experimental observation.

There are no special requirements for taking this course, apart from a good knowledge of quantum physics (e.g. from the "Advanced Quantum Physics" Part II course). Supervisions will be done in groups of 6-8 students.

Introduction and revision of basic concepts: Bohr’s theory, Einstein A&B coefficients, Stern-Gerlach experiment

Atomic structure: Hydrogen atom, fine structure, Lamb shift, hyperfine structure, electric dipole transitions, selection rules, Zeeman effect, magnetic dipole transitions, alkali atoms

Fundamentals of atom-laser interaction: Driven two-level system, Ramsey spectroscopy and atomic clocks, density matrix, optical Bloch equations, dissipation, cross-sections & line shapes, Doppler-free laser spectroscopy, ac Stark effect, two-photon and Raman transitions

Laser cooling & trapping: Scattering force, slowing of atomic beams, optical molasses, Dop- pler cooling limit, magneto-optical trap, optical dipole trap, Sisyphus cooling below the Doppler limit

Evaporative cooling and Bose-Einstein condensation of atomic gases: Requirements, magnetic trapping, evaporative cooling, critical temperature, condensate fraction, experimental observation of Bose-Einstein condensation

Properties of atomic Bose-Einstein condensates: Atomic interactions, macroscopic wave function, matter-wave interference of Bose-Einstein condensates, Gross-Pitaevskii equation, Thomas-Fermi approximation, Bogoliubov excitation spectrum, superfluidity

BOOKS

Atomic Physics, Foot C J, (Oxford University Press) Laser Cooling and Trapping, Metcalf H & van der Straten P (Springer - Verlag) Bose-Einstein Condensation in Dilute Gases, Pethick C J & Smith H (CUP)

Part III Physics – Major Topics 85 PARTICLE PHYSICS

C G Lester

The Part III Particle Physics Major option course aims to provide a reasonably complete description of our understanding of modern particle physics. The Part II Particle and Nuclear Physics course is not a prerequisite to this course although familiarity with basic particle physics termi- nology is assumed. The course will concentrate on the Standard Model with the aim of providing both a detailed description of current experimental data, and the theoretical understanding to place these experimental results in context. The Minor Option course on “Gauge Field Theory” covers particle physics theory at a more advanced level.

Introduction, cross sections and decay rates: The structure of the Standard Model; revision of basic concepts; relativistic phase space and its role in two-body decays and two-body scattering.

Solutions to the Dirac equation: The Klein-Gordon equation; the Dirac equation and Dirac spinors; negative energy solutions and anti-particles; C and P symmetries; spin and helicity.

Interaction by particle exchange and QED: interaction by particle exchange; the QED ver- tex; Feynman rules for QED; scattering and e+e– annihilation in QED; the role of spin and helicity in QED and chirality; QED calculations using Dirac spinors.

Electron proton scattering: Rutherford scattering revisited; low energy electron proton scattering and form factors; deep inelastic scattering and structure functions; Bjorken scaling and the Callan-Gross relation; the quark-parton model; valance and sea quarks.

The quark model and QCD: symmetries and conservation laws; SU(3) flavour symmetry; mesons and baryon wave; SU(3) colour symmetry; confinement and gluons; Feynman rules for QCD; colour factors; the QCD potential; running couplings and asymptotic freedom; experimental evidence for QCD.

Particle Detectors: Particle interactions in matter, particle detection and large detectors at modern particle colliders.

Charged-current weak interactions: V-A Theory and parity violation; helicity structure of the weak interaction; lepton universality; neutrino scattering; neutrino structure functions and the anti-quark content of nucleon.

Neutrino physics and neutrino oscillations: Neutrino interactions; detecting neutrinos; solar and atmospheric neutrinos; neutrino oscillations and the PMNS matrix; CP and CPT in the weak interaction; recent neutrino experiments.

The CKM matrix and CP violation: The Cabibbo angle and the CKM matrix; CP violation in the early universe; the neutral kaon system and strangeness oscillations; CP violation in the kaon system; the CKM matrix and CP violation in the Standard Model.

Electroweak Unification and the Standard Model: W boson decay; the W and Z bosons and a unified electroweak theory; the Z resonance; precision tests of the electroweak theory at LEP; the Higgs mechanism; hunting the Higgs; problems with the Standard Model.

86 Part III Physics – Major Topics BOOKS

There are many books available on particle physics, at various levels. The following are suggested as useful for this course: Particle Physics, Martin B R and Shaw G (2nd edn Wiley 1997). A good introductory text, more suited to Part II but covers most of the basic material. Introduction to High Energy Physics, Perkins D H (4th edn CUP 2000). Good coverage of experimental techniques and some aspects of theory. A slightly lower level than this course with a more historical approach. Introduction to Elementary Particles, Griffiths D (Harper & Row 1987) out of print Theoretical treatment, going slightly beyond the level of this course, but well written and clear. Good reference for those wishing to pursue some of the mathematical details. Quarks and Leptons, Halzen F and Martin A D (Wiley 1984). Goes beyond the level of this course, but provides a good description of the underlying theoretical concepts.

Part III Physics – Major Topics 87 PHYSICS OF THE EARTH AS A PLANET

K Priestley, J Rudge and A Deuss

Our aim in this course is to show how concepts from physics, especially from classical physics and continuum mechanics, can be used to understand the structure and evolution of the Earth, and to a lesser extent, the other terrestrial planets. Our approach is different from that taken in Part IA Geology, and does not assume knowledge of the material in that course. The course is mainly intended for students who are theoretically inclined. It includes practicals, which are designed to help students understand concepts discussed in the lectures. These practicals are like those in IA Geology, or the unassessed practicals in IA Materials and Minerals, in that they are not “written up” and demonstrators are present to help with any problems. An understanding of the concepts involved in the practicals will be tested in the written examination. Some of the lectures will be given by the other members of the Department of Earth Sciences whose present research is concerned with the topics that are part of the course.

Introduction to geophysics: Theories of planetary formation, composition of terrestrial planets and the bulk composition of the Earth, origin of the crust, mantle, and core, large scale static structure of the Earth.

Plate tectonics: Rotation vectors and poles of rotation, triple junctions, present-day plate motion, reconstructing past plate motions.

Continuum mechanics: Fundamental laws of continuum mechanics, analysis of stress, deformation and strain.

Seismology and elastic wave propagation: Linearised theory of elasticity and the wave equation, P and S waves, Eikonal equation and geometrical ray theory, partitioning of seismic energy at a boundary, ray characteristics in simplified flat and spherical Earth models, and surface wave propagation.

Earth structure: Travel time curves; group and phase velocity dispersion curves; travel time, dispersion and waveform inversion for velocity structure; velocity structure of the crust, mantle and core.

The earthquake source: Earthquake locations, fault plane solutions, the seismic moment tensor, earthquake dynamics, body wave and surface wave modelling, earthquake mechanisms and crustal deformation.

Thermal and mechanical structure of plates: Structure of oceanic and continental plates, isostasy and gravity, thermal models, depth of the oceans, subduction, basin formation, the elastic layer on Earth and Venus.

Dynamic processes: Heat sources of Earth and Venus, thermodynamics of convection, convective regime of the mantle, the cooling of the mantle, thermal history of the mantle.

Immediately after the Michaelmas term is over, Part II students in the Department of Earth Sci- ences take a week long tectonics field trip to Greece. This is an excellent way to see first hand the surface manifestation of earthquake faulting and other geophysical topics discussed from a more theoretical viewpoint in the Physics of the Earth as a Planet lectures. Students taking this Part III Physics course are welcome to come on the Greece field course but the field trip is not connected to the Physics of the Earth as a Planet lectures as such. The cost for the trip is around £85.

88 Part III Physics – Major Topics BOOKS

The solid Earth, Fowler C M R (2nd edn CUP 2004) This is an excellent general book on geophysics. It covers about half of the course, but uses less mathematics than we do. Fowler’s discussion of seismology is briefer than that of the present course, and she does not discuss mantle convection and dynamics at all. Introduction to Seismology, P M Sheaver (CUP 1999) This text covers most of the material discussed in the course lectures on seismology. Geodynamics, Turcotte D L & Schubert G (Wiley 2002) This covers much of the material of the course except seismology, at about the same mathematical level that we will use. It contains many problems with their solutions.

Part III Physics – Major Topics 89 QUANTUM CONDENSED MATTER FIELD THEORY

B D Simons

As well as Part IB NST mathematics, the course will assume a basic knowledge of Lagrangian, statistical, and quantum mechanics. Exposure to the Part II theory courses (TP1 and TP2) and Quan- tum Condensed Matter course is useful but not essential.

Collective Phenomena - From Particles to Fields: Linear harmonic chain and free scalar field theory; functional analysis; quantisation of the classical field; phonons; relation to quantum electrodynamics; concept of broken symmetry, collective modes, elementary excitations and universality.

Second Quantisation: Fock states; creation and annihilation operators for Bose and Fermi systems; represention of one and two-body operators; canonical transformations; Applications to the interacting electron gas; Wannier states, strong correlation and the Mott transition; quantum ferromagnetism and antiferromagnetism, spin representations and SU(2) spin algebra, spin- waves; †spin liquids; weakly interacting Bose gas.

Path Integral Methods: Propagators and the construction of the Feynman Path integral; Gaussian functional integration, stationary phase and saddle-point analyses; relation to semi- classics and statistical mechanics; quantum harmonic oscillator and the single well; double well, instantons, and tunnelling phenomena; †metastability.

Many-Body Field Integral: Bose and Fermi coherent states; Grassmann algebra; coherent state path integral; quantum partition function; Bogoluibov theory of the weakly interacting Bose gas and superfluidity; Cooper pair instability, and the BCS theory of superconductivity; Ginzburg- Landau phenomenology and the connection to classical statistical field theory; †Gauge theory and the Anderson-Higgs mechanism; †Resonance superfluidity in ultracold atomic gases and the BEC to BCS crossover.

Italics denote specific mathematical topics. Items marked † will be largely used as source material for problem sets and supervision.

Learning aims: By the end of this course, you will be familiar with the basic foundations of qua- tum field theory including the method of second quantisation, the Feynman path integral, and field integral techniques. On the Feynman path integral, you will be able to address the quantum mechanics of single particle systems from the physics of bound state systems to the estimation of tunnelling rates in unbound systems. On the field integral, you will be able to formulate the coherent state path integral of many-particle bosonic and fermionic systems. In particular, you will be able to address the quantum mechanics of superfluid and superconducting systems. Finally, you will have an appreciation of how the concepts of quantum field theory provide a common language to address phase transitions and collective phenomena in both high and low energy quan tum many-particle systems.

BOOKS

Condensed Matter Field Theory, Altland A and Simons B D (CUP 2006). Statistical Mechanics, Feynman R P and Hibbs A R (McGraw-Hill 1965). Quantum Field Theory in Condensed Matter Physics, Nagaosa N (Springer 1999). Quantum Many-Particle Systems, Negele J W and Orland H (Addison-Wesley 1988). Techniques and Applications of Path Integration, Schulman L S (Wiley 1981). The Physics of Quantum Fields, Stone M. (Springer 2000). Path Integrals in Quantum Mechanics, Zinn-Justin J (Oxford Graduate Texts 2004). Lectures on Statistical Physics, Levitov L S (http://www.mit.edu/~levitov/8.334/)

90 Part III Physics – Major Topics QUANTUM FIELD THEORY

M J Perry (Part III Maths)

Quantum field theory is the language in which much of modern physics is formulated. It provides a synthesis of quantum theory and special relativity and offers a mathematical framework in which to describe many particle systems. This course is an introduction to quantum field theory using the canonical quantization approach in which classical degrees of freedom are replaced by operators.

This course requires a high-level of mathematical facility.

Classical Field Theory: Lagrangian field theory, Symmetries, Noether’s theorem and conserved currents, Hamiltonian field theory.

Canonical Quantization: The Klein-Gordon equation, Free quantum fields, Vacuum energy, Emergence of particles, The Heisenberg picture, Causality and propagators, Applications, Non- relativistic field theory.

Interacting Fields: Types of interaction, The interaction picture, Dyson’s formula, Scattering, Wick’s theorem, Feynman diagrams and Feynman rules, Amplitudes, Green’s functions, Con- nected diagrams and vacuum bubbles.

The Dirac Equation: The Lorentz group, Clifford algebras, Spinor representation, The Dirac Lagrangian, Chiral spinors, The Weyl equation, Symmetries and currents.

Quantizing the Dirac Field: A glimpse at the spin-statistics theorem, Fermionic quantization, Fermi-Dirac statistics, Propagators, Particles and anti-particles, Dirac’s hole interpretation.

Quantum Electrodynamics: Gauge invariance, Quantization, QED, Lorentz invariant propagators, Feynman rules, Processes in QED involving electrons, positrons and photons.

BOOKS

An Introduction to Quantum Field Theory, Peskin M E and Schroeder D V (Addison-Wesley 1996) A very clear and comprehensive book. To a large extent, the course will follow the first section of this book. Quantum Field Theory, Ryder L H (2nd edn CUP 1996) An elementary text covering most of the material in this course. Quantum Field Theory in a Nutshell, Zee, A (Princeton University Press 2003). A charming book, where the emphasis is placed on physical understanding and the author isn’t afraid to hide the ugly truth when necessary. However, Zee primarily uses the path integral approach which we won’t cover in this course. The Quantum Theory of Fields, Vol 1. Weinberg S (CUP 1995). Weinberg takes a unique route through the subject, focussing initially on particles rather than fields.

There is a course webpage with lecture notes at: http://www.damtp.cam.ac.uk/user/tong/qft.html

Part III Physics – Major Topics 91 RELATIVISTIC ASTROPHYSICS AND COSMOLOGY

A C Fabian and A N Lasenby

This course builds on material from the Part II Relativity course. It will be helpful to have taken Astrophysical Fluid Dynamics in Part II.

Introduction: The main constituents of the Universe: solar system, stars, nebulae, star clusters, galaxies, clusters, radio sources, quasars etc. Sizes, velocities, masses, luminosities. The distance scale.

General Relativity: Review of foundations of general relativity: equivalence principle, strong and weak forms, curved spaces, the geodesic equation, the field equations, Schwarzschild solution.

Stars, white dwarfs, neutron stars: The physics of stars and stellar evolution, stellar structure, white dwarfs and the Chandrasekhar mass. General relativistic treatment of stellar structure, the Oppenheimer-Volkoff equations. Neutron star structure, mass-radius relation for cold matter, pair production and annihilation.

The end-points of stellar evolution: Supernovae, pulsars, supernova remnants, shock waves, accretion, accretion discs, the Eddington limit. X-ray binaries, the Crab Nebula, binary and milli- second pulsars, tests of general relativity.

Black holes: Formation, observational evidence, accretion discs, effects of spin.

Active Galactic Nuclei (AGN): Radiation processes, energy budget, Eddington limit and growth. Special relativistic effects in jetted sources. Gamma-ray bursts.

Gravitational waves: wave solutions to Einstein’s equations in vacuum. Detection of gravitational waves. Astrophysical sources of radiation.

Galaxies and clusters of galaxies: Observational properties and structure. Black hole feedback. Evidence for dark matter. Gravitational lenses, rotation curves.

The Robertson-Walker metric: Basic observations. Hubble’s law, isotropy and homogeneity of the Universe, comoving coordinates and spatial curvature, redshift. Distance measures, decel- eration parameter, luminosity-redshift and angular diameter-redshift relations. Observed flux versus redshift relations. Number counts.

The standard Friedmann models: General solutions, cosmological constant, the redshift- cosmic time relation, horizons, the flatness and isotropy problems. Ages of stars and galaxies. Methods for determining the Hubble constant.

The Microwave Background Radiation: Evolution of blackbody spectrum. Energy densities, recombination and timescales. Imprints on the CMB and relation to the growth of structure.

The Early Universe: Nucleosynthesis, baryon asymmetry. Inflation and the problems it addresses. Origin of perturbations. Cosmological parameters and observations. Clues to the earliest times, links with fundamental theory.

92 Part III Physics – Major Topics BOOKS

At roughly the level of the course: Essential Relativity, Rindler W (2nd edn Springer 1990). Good introduction to GR and cosmology. Principles of Cosmology and Gravitation, Berry M V (2nd edn IoP 1989). Elementary but clear introduction to GR and cosmology, taking similar line to that used in course. Black holes, White Dwarfs and Neutron Stars (The Physics of Compact Objects), Shapiro S L & Teukolsky S A (Wiley 1983). Good textbook for parts of course. Aimed at advanced physics students. Accretion Power in Astrophysics, Frank J, King A & Raine D (2nd edn CUP 1992). Useful for high energy astrophysics aspects. High Energy Astrophysics, Vols 1 and 2, Longair M S (2nd edn CUP 1992 1994). Useful chapters. Exploring Black Holes: Introduction to General Relativity, Taylor E F & Wheeler J A (Addison- Wesley 2001). Supplementary reading at an elementary level: The Physical Universe, Shu F (University Science Books 1982). Excellent introduction to the whole field of astrophysics and cosmology. The Big Bang, Silk J (2nd edn Freeman 1989). Our Evolving Universe, Longair M S (CUP 1996) Black Holes, Luminet J (CUP 1992). Excellent paperback account of black holes Gravity’s Fatal Attraction: Black Holes and the Universe, Begelman M C and Rees M (Freeman: Scientific American 1996) More advanced books covering General Relativity in greater detail: Introducing Einstein’s Relativity, d’Inverno R (OUP 1995) Introduction to Cosmology, Narlikar J V (2nd edn CUP 1993) General Relativity: An Introduction for Physicists, Hobson M P, Efstathiou G P & Lasenby A N (CUP 2006)

Part III Physics – Major Topics 93 SOFT MATTER AND BIOLOGICAL PHYSICS

U Keyser and R Goldstein

This course will assume knowledge of the topics covered in the Part IB Mathematics or Part IB Mathematical Methods courses, respectively. In addition, students should prepare material on partial differential equations as discussed for example in Chapters 20 & 21 of Riley, Hobson and Bence "Mathematical Methods for Physics and Engineering".

Microscopic physics Poisson Boltzmann equation, Debye Huckel, surface potentials, Poisson-Boltzmann equation in spherical, cylindrical geometry, Manning condensation of long chain molecules, Brownian motion, fluctuation-dissipation theorem.

Fluctuation induced forces Review of polymer physics, freely jointed chains, worm-like chains, single chain experiments, pro- tein unfolding, Van der Waals interaction, attraction of neutral objects of arbitrary shape, DLVO theory.

Elasticity Curve dynamics, Lagrangian dynamics, general 2-dimensional curves, curve shortening equation, global constraints, space curves, vortex rings, viscous drag, elastic coefficients , Elastohydrody- namics, Stokes equation, reversibility, Euler Buckling, Strain and Stress tensor, generalization of Hooke’s Law, Twisted worm-like-chain.

Chemical kinetics and pattern formation Michaelis Menten Kinetics, cooperativity, slaving, diffusive effects in pattern formation, instabilities, reaction diffusion systems, Fitz-Hugh Nagumo model, separation of timescales, front dynamics, bioconvection, gyrotaxis.

Membrane transport Passive diffusion- and energy-driven transport, nucleo-cytoplasmic transport, Diffusion through membranes, lipophilic ions, ionchannels, ionophores.

Electrokinetic effects Polymer dynamics in gels, electrophoresis-/osmosis in channels, pressure driven flows, streaming currents and potentials, electrokinetic and hydrodynamic effects in confinement, nanopores.

Introductory Reading Biological Physics, P. Nelson, W. H. Freeman (2007) Mathematical Biology I. and II., J. D. Murray, Springer (2007, 2008) Molecular Driving Forces, K. Dill and S. Bromberg, Garland Science (2009)

Advanced and Complementary Reading Soft Condensed Matter Physics in Molecular and Cell Biology, D. Andelman & W. Poon, Taylor & Francis (2006) Van der Waals Forces, A. Parsegian, CUP (2005) Intermolecular and Surface Force, J. N. Israelachvili, Academic Press (1992) The Theory of Polymer Dynamics, M. Doi & S. Edwards, OUP (1986) Theory of the Stability of Lyophobic Colloids, E. Verwey and J. Overbeek, Elsevier (1948)

94 Part III Physics – Major Topics ATMOSPHERIC PHYSICS

M Herzog and H Graf

The course is split into two parts. In the first part the principles of atmospheric physics will be introduced followed by an overview of mean circulation and climate variability. The second part focuses on cloud physical processes and their treatment in numerical models. The titles of the lectures are as follows:

1. Thermodynamics of the atmosphere 2. Atmospheric radiation 3. Basics of hydrodynamics 4. Vorticity and divergence 5. Waves in the atmosphere 6. General atmospheric circulation 7. Energy cycle in the atmosphere 8. Atmospheric ocean coupling, ENSO 9. Teleconnections, e.g. NAO 10. Climate system modelling 11. Clouds - classification and types 12. Cloud microphysics 13. Cloud dynamics 14. Cloud modelling 15. Cloud parameterization 16. Open science problems, e.g. aerosol cloud interaction

Lectures 1. to 6. and 11. to 16. will be given by Michael Herzog, lectures 7. to 10. by Hans Graf.

BOOKS

An Introduction to Atmospheric Physics. David G. Andrews, Cambridge University Press, 2005.

A Short Course in Cloud Physics. R. R. Rogers and M. K. Yau, Elsevier Science, 1996.

Global Warming, Understanding the Forecast. David Archer, Blackwell Publishing, 2008.

Part III Physics – Minor Topics 95 BIOLOGICAL PHYSICS

E Nugent

This course is an introduction to the physics of biological systems at the molecular and cellular level. The emphasis is on the design principles that living systems use to accomplish multifarious cellular processes, enabling them to sense and react to their environment. A set of case studies aims to demonstrate how physicists’ experience of the behaviour of complex systems can complement experimental investigations by biologists to explain how living systems work, and why biology is the way it is. The course also introduces some of the methods currently used in biological physics. Exposure to material from the Part II Soft Condensed Matter and Biophysics course will be beneficial.

Cells: What's in a cell? Component molecules. Cellular processes. Significance of Brownian motion, noise and stochasticity.

Information and Regulation: DNA replication. RNA, transcription and translation. Promotors, repressors and operons, DNA topology.

Structural elements 1: Lipid bilayer, membranes and vesicles. Endocytosis and trafficking.

Energy: Chemiosmotic theory. Membrane potential, Nernst relation, ion channels and pumps. Me- tabolism and the synthesis of ATP.

Structural elements 2: The cytoskeleton: mictrotubles, actin filaments, networks and gels. Cell movements and locomotion.

Molecular machines: Motor proteins and isothermal ratchets. Mechanochemistry and the Kramers equation. Muscle contraction. Processive motors. Rotary motors.

Sensory cells: Hair cells in the ear. Active signal detection and cochlear mechanics. Phototransduc- tion in the retina.

Nerve impulses: Axons and the action potential. Hodgkin-Huxley model. Spiking and bursting.

Methods 1: Light microscopy, fluorescence microscopy, confocal and multiphoton microscopy, FRET, FRAP.

Methods 2: Optical tweezers, other optical traps, atomic force microscopy and single molecule experiments.

BOOKS

Essential Cell Biology, Alberts B et al. (Garland 2003). Biological Physics: Energy, Information, Life, Nelson P (WH Freeman 2003). Cell Movements, Bray D (Garland 2000). Mechanics of Motor Proteins and the Cytoskeleton, Howard J (Sinauer 2000)

96 Part III Physics – Minor Topics FORMATION OF STRUCTURE IN THE UNIVERSE

R Maiolino

This course builds on material in the Relativistic Astrophysics and Cosmology Major option and discusses how structure forms in the universe on all scales from planets and stars, through galaxies to the largest structures we know about. Throughout the course we develop physical models motivated by the evidence from a wide range of observational data we now have available. The topics covered are at the forefront of active research in astrophysics and failings of our current understanding and models will be discussed along with likely developments in the near future.

It is assumed that students have taken Astrophysical Fluid Dynamics in Part II.

Introduction: overview of the evolution of structure in the universe; properties of galaxies in the local universe; star-forming regions; a first-look at the high-redshift universe.

Physical processes in baryonic gas: heating processes; cooling processes; cooling curves; thermal stability and instability; multi-phase medium in galaxies; baryonic gas in the early universe.

Gravitational stability and instability: the isothermal sphere as a simple model; virial equilibrium; Jeans analysis in an infinite medium; role of magnetic fields, turbulence and angular momentum.

Formation of stars and planets: inside-out collapse; formation of the first core and second core; deuterium burning; hydrogen burning; angular-moment, discs and stellar jets; planet formation; extra-solar planets.

Star-formation on galactic scales: properties and structure of star-forming galaxies; initial mass functions; factors controlling star formation; Schmidt-Kennicutt star-formation law; starbursts; a first look at star formation histories.

Cosmological origins of structure: Origin and early growth of density perturbations and the matter power spectrum.

Galaxy formation: collapse of a spherical over density; evolution of the baryonic gas; numerical simulations; hierarchical structure formation; failure of the simple model; the need for feedback; supernova feedback; AGN feedback; improved models for galaxy evolution; galaxy dynamics.

The high-redshift universe and galaxy evolution: properties of galaxies at high redshift; Lyman-break galaxies; the Hubble deep field; old red galaxies; evolution of the AGN population; evolution of the galaxy population; confronting predictions and observations.

Large-scale structure: clusters and superclusters; correlation functions; remnants of primor- dial structure; the cosmic web.

Challenges: problems with our current models of galaxy formation; the end of the dark ages – the epoch of re-ionisation; the equation of state of dark energy; testing our predictions.

Part III Physics – Minor Topics 97 BOOKS

The physics of the interstellar medium, Dyson J E and Williams D A (2nd edition IoP) Accretion processes in star formation, Hartmann L (Cambridge) An introduction to modern cosmology, Liddle A (2nd edition Wiley) – a good and relatively simple text to put material in context The Structure & Evolution of Galaxies, Philips S (Wiley) Galaxy formation, Longair M S (2nd edition Springer) Cosmology – the origin and evolution of cosmic structure, Coles P and Lucchin F (2nd edition Wiley) – a more advanced text

98 Part III Physics – Minor Topics GAUGE FIELD THEORY

B M Gripaios

This course is an introduction to the gauge field theories of modern Particle Physics, focusing on the gauge-invariant Lagrangian of the Standard Model of electroweak and strong interactions, with particle masses introduced via spontaneous symmetry breaking (the Higgs mechanism). There are no formal prerequisites for the course though it would be helpful to have attended the Part III Particle Physics or Quantum Field Theory Major Options; for those who have not, the lectures cover the essential material, including the necessary relativistic quantum field theory.

Relativistic quantum mechanics: Covariant notation; transition rates; phase space; two-body decay and scattering; interaction and scattering via particle exchange; Feynman graphs; Klein-Gordon equation; Dirac equation; free-particle spinors; helicity and chirality; electromagnetic interactions, photons; charge conjugation; gamma matrix algebra; Compton scattering.

Relativistic quantum fields: Classical field theory, Lagrangian densities; Klein-Gordon field; Fou- rier analysis; second quantization; single-particle and two-particle states; quantising the electromagnetic field; vacuum energy and normal ordering; complex fields; symmetries and conservation laws; Noether’s theorem; Dirac field; spin-statistics theorem; Majorana fields.

Gauge field theories: Gauge symmetry in QED; non-Abelian gauge symmetry; strong interactions, QCD; weak interactions; electroweak interactions; spontaneous symmetry breaking; gauge boson masses; the unitary gauge; Yukawa interactions, quark and lepton masses; Higgs mechanism; parameters of the Standard Model; properties of the Higgs boson.

Renormalisation: Ultraviolet divergences; renormalisability; dimensions of fields and couplings; non-renormalisable interactions and effective theories.

Beyond the Standard Model: neutrino masses, the seesaw mechanism; grand unification, SU(5).

BOOKS

Quantum Field Theory, Mandl F and Shaw G (2nd edn Wiley 2009) A Modern Introduction to Quantum Field Theory, Maggiore M (OUP 2005) Gauge Theories in Particle Physics, Aitchison I J R and Hey A J G (3rd edn 2 vols IoP 2003) An Introduction to Quantum Field Theory, Peskin M E and Schroeder D V (Addison-Wesley 1995)

Part III Physics – Minor Topics 99 MEDICAL PHYSICS

Dr S Bohndiek and Others

This course is intended to give an overview of some of the Medical applications of Physics. Most of the lectures are given by Addenbrookes Hospital staff. The material should be accessible to all Part III students.

Introduction: The scope of medical physics, introduction to the biological problem, radiation terms and units, statutory responsibilities.

Mechanisms of energy loss by ionising radiation in biological materials: Classical calculation of energy loss by heavy charged particles, extension to electrons, ranges of charged particles and Bragg curves. Interaction of neutrons with matter. Mechanisms of energy loss by electromagnetic radiation. X-ray production (kilovoltage and Megavoltage). Radiation dosimetry.

Use of X-rays for diagnosis: X-ray imaging: X-ray image transducers and image intensifiers; assessment of image quality and the modulation transfer function. Mammography. X-ray computed tomography. Patient dose measurement and typical doses in diagnostic radiology. Radiation Protection.

Imaging with radioactive tracers: Single-photon imaging: optimal tracer properties; photon detection using a gamma camera; acquisition modes. Tomographic image reconstruction: data required for tomography; analytical and iterative reconstruction algorithms. Positron-emission tomography (PET): cyclotron production of positron-emitters; positron emission and annihilation; detection of annihilation photon pairs; acquisition modes; image reconstruction and data corrections.

Diagnostic ultrasound: Interaction of ultrasound with tissue; ultrasound transducer and the ultrasound field; A-, M-, B-modes and real-time imaging; common image artefacts; Doppler techniques; safety considerations; clinical examples.

Magnetic resonance imaging and spectroscopy: Controlling the magnetic nucleus, proton density T1 and T2 measurements, the imaging process, coil design, field strength and safety considerations, MR spectroscopy.

Combining imaging modalities: Techniques for image registration. Combining images from multiple modalities.

Radiotherapy: Introduction to radiobiology. Relative biological effectiveness. Choice of radiation for radiotherapy. Medical linear accelerators. Radiotherapy treatment planning with external beams. Use of CT and MR images in treatment planning. Radiation distribution around closed sources, source distributions and dose specification, equipment and clinical applications.

100 Part III Physics – Minor Topics BOOKS

The physics of radiology, Johns H E & Cunningham J R (4th edn Charles C Thomas 1983). This is a good general text on the interaction of radiation with matter, and on radiotherapy physics. See particularly Chapters 2.8-2.11, 3, 4.1-4.5, 5, 6, 15.

The physics of medical imaging, Webb S (ed) (IoP Publ. 1988). This is a good general text for the imaging part of the course, particularly chapters 2, 3, 4, 6, 7 & 8.

Physics for Medical Imaging, Farr R F and Allisy-Roberts P J (Saunders 1997)

Radionuclide Imaging Techniques, Sharp P F, Dendy P P & Keyes W I (Academic Press 1985). See particularly chapters 2 & 3.

Diagnostic ultrasonics; principles and use of instruments, McDicken W N (3rd edn Churchill Living- stone 1991). Several chapters are relevant, but especially 3, 4, 8 & 11.

The Physics of Radiotherapy X-rays from linear accelerators. Metcalf P, Kron T and Hoban P. (Medi- cal Physics Publishing 1997)

Physics for Diagnostic Radiology, Dendy P P and Heaton B (2nd edn IOP Publishing 1999). A good general introduction to diagnostic imaging before consulting other references for more detailed physics.

The Theory and Practice of 3D PET, Bendriem B and Townsend D W (eds) (Kluwer Academic 1998). Covers scanner design, data acquisition, image reconstruction and image quantitation.

Atlas of Clinical Positron Emission Tomography, Maisey M N, Wahl R L and Barrington S F (Arnold 1999). Up-to-date coverage of the clinical applications of PET.

Magnetic Resonance Imaging: Physical Principles and Sequence Design, Haacke E M, Brown R W, Thompson M R and Venkatesan R (Wiley 1999). A very comprehensive technical reference.

MRI from Picture to Proton, McRobbie D W, Moore E A, Graves M J, Prince M R (CUP 2006). A very readable, recent book, with a clinical bias which includes some of the basic physics.

Part III Physics – Minor Topics 101 NONLINEAR OPTICS AND QUANTUM STATES OF LIGHT

M Atature

These minor option lectures will provide a basic overview on the field of nonlinear optics from classical to quantum-mechanical descriptions of light. A survey of key nonlinear optical processes will be covered and recent advances of the field leading to the generation of nonclassical states of light dis- playing squeezing and entanglement will be discussed.

Introduction: Historical development of nonlinear optics, physical origins of nonlinear response, anharmonic oscillators, coupled wave equations, classical and quantum mechanical derivation of nonlinear optical susceptibility, symmetry properties of nonlinear susceptibilities.

Second-Order Nonlinear Interactions: second harmonic generation, depleted pump effects, Gaussian beams, pulse propagation in nonlinear medium.

General Parametric Processes: up-conversion, amplification, optical gain, sum- and difference- frequency generation, phase matching, quasi-phase matching.

Ultrafast Pulse Phenomena: amplitude and phase measurement of optical pulses using nonlinear optics, frequency-resolved optical gating and other techniques.

Nonlinearities in Refractive Index: Third-order nonlinearity, Kerr medium, intensity dependence and self-phase modulation, self-focusing, optical filamentation, soliton formation.

Nonclassical light: quantization of electromagnetic waves, parametric fluorescence, squeezed light, quantum correlations and photon statistics, Fock, thermal and coherent states of light, superposition and entanglement, vacuum field and spontaneous emission.

Supervisions: The course will include 3 supervisions to cover example problems and supplementary concepts.

BOOKS

Primary: Principles of Nonlinear Optics, Y. R. Shen, Wiley-Interscience, 1984. Nonlinear Optics, R. W. Boyd, Academic Press, 2003.

Auxiliary: Quantum Theory of Light, R. Loudon, OUP, 2000. Optical Coherence & Quantum Optics, L. Mandel & E. Wolf, CUP, 1995. Quantum Electronics, A. Yariv, John Wiley & Sons, 1989.

102 Part III Physics – Minor Topics PARTICLE ASTROPHYSICS

M A Parker

This course will give a basic introduction to experimental and theoretical aspects of particle astrophysics. The aim of the course is to emphasise the connection between the very large (cosmology) and the very small (particle physics) and to demonstrate that the early Universe provides the `ultimate' particle accelerator, giving access to energies that will never be created by machines on Earth.

Overview of astroparticle physics: Links between particle physics and cosmology, the big open questions.

The thermal history of the Universe: Timeline and concept of freezeout. Synthesis of light elements. The mystery of baryon asymmetry, Sakharov criteria.

CP violation and baryogenesis: How CP violation can create baryons. Experimental evidence for CP violation. CP violation in SUSY models.

The matter content of the Universe: Evidence for dark matter, possible explanations, current searches. Dark energy.

Inflation: Horizon and flatness problem, inflation, reheating. Problems of Higgs field in the early universe. Use of CMB fluctuations as a cosmological probe.

Relics from the Early Universe: Dark matter abundance, monopoles, cosmic strings and textures. Comparison of WMAP results with SUSY models and HEP constraints.

Cosmic rays: spectrum, GKZ cut-off, astrophysical sources and acceleration mechanisms.

Neutrinos: neutrino fluxes, detection, neutrino oscillations and masses. Double-beta decay experiments, astrophysical constraints on neutrino masses. Relic neutrinos.

Modified gravity: Gravitational waves. MOND. Extra dimensions, brane-worlds. Tests of short-range gravity.

Black holes: Black holes, hawking radiation, quantum black holes.

BOOKS

Particle Astrophysics, Perkins D (Oxford University Press). This is available in paperback and is pitched at about the right level for the course, though it does not cover inflationary cosmology in much detail.

Cosmology and Particle Astrophysics, Bergström L and Goobar A (Wiley 1999). Dated and has more advanced material than is required for the course.

The Physical Foundations of Cosmology, Mukhnaov V (CUP 2005). Graduate level text, but with useful pedagogical discussions of nucleosynthesis and baryogenisis.

The Early Universe, Kolb E and Turner M (Westview Press 1994). The classic graduate text, but now very dated.

Part III Physics – Minor Topics 103 SUPERCONDUCTIVITY AND QUANTUM COHERENCE

G G Lonzarich

The course presents a unified treatment of superconductivity, superfluidity and Bose-Einstein condensation as an introduction to the general problem of quantum coherence. It is assumed that students taking this course will have also done Advanced Quantum Condensed Matter Physics.

Introduction to Superconductivity: Historical overview; superconducting materials; macroscopic properties; Meissner effect and levitation; type-I and type-II states; Landau theory; critical field Bc.

Ginzburg-Landau Theory: The Ginzburg-Landau free energy and Ginzburg-Landau equations; London equations; penetration depth and coherence length; gauge transformations and gauge symmetry breaking (broken symmetry in internal space).

Vortex Matter: Flux quantization; vortex lines and vortex lattice; the critical fields Bc1 and Bc2, type- I and type-II superconductivity; vortex pinning and critical currents; vortex liquid state.

Josephson Effect and SQUIDs: DC and AC Josephson effects; gauge invariant phase; quantum interference for weak links; the DC SQUID; applications.

Superfluidity: Phenomenology; superfluid wavefunction; two-fluid model and the fountain effect; flow quantization and vortices; first and second sound; rotons; Landau’s critical velocity.

Bose-Einstein Condensation (BEC): Ultra-cold atomic gases; BEC with weak interactions; coherent states and second quantization; the Bogoliubov Theory and connection to the phenomenological Ginzurg-Landau Theory.

The Bardeen-Cooper-Schrieffer (BCS) Theory: BEC to BCS cross-over; Cooper pairs; the BCS wavefunction; the Bogoliubov quasiparticles and the energy gap; experimental evidence for the validity of the BCS theory; order parameter and the Ginzburg-Landau coherence length.

Current Problems in Superfluidity and Superconductivity: Unconventional forms of quan- 3 tum order; p-wave spin-triplet superfluidity in He; spin-triplet superconductivity in Sr2RuO4 and UGe2; d-wave superconductivity in the high Tc cuprates; phase-sensitive measurements of the gap ani- sotropy; the pseudo-gap state; unconventional mechanisms for superconductivity; collective modes in superfluids and superconductors; the Anderson-Higgs mechanism and superconductivity.

BOOKS

Superconductivity, Superfluids and Condensates, Annett J F (Oxford University Press, 2004) Superconductivity of Metals and Cuprates, Waldram J R (Institute of Physics Publishing, 1996)

Also:

Bose-Einstein Condensation in Dilute Gases, Pethick C J and Smith H (Cambridge University Press, 2002) Introduction to Superconductivity, Tinkham M (McGraw-Hill, 1996)

104 Part III Physics – Minor Topics THE FRONTIERS OF OBSERVATIONAL ASTROPHYSICS

R D E Saunders

The course is an entry to the observational and analysis techniques of astrophysics and cosmology. It outlines the underlying physics and studies example issues at the forefront of current research. It is about exactly what limits what we know about the Universe and why.

The material is not covered in the Relativistic Astrophysics and Cosmology major option and so com- plements that option, and by the same token it doesn’t matter if you didn’t attend that option. Indeed, it doesn’t matter whether or not you took the Astrophysical Fluids option last year nor how well you fared with the Relativity course.

Introduction: Some basics. The mass-radius relationship of everything.

Observational design and statistical inference: The replacing of lab measurements by the study of samples of objects. Hidden correlations and Malmquist bias. Eddington bias. Completeness and false detection. Selection effects: the critical problems in trying to measure apparently simple things such as the space density of quasars as a function of their power outputs and the space density of planets as a function of their masses. Model fitting, chi-squared, likelihood function, etc. Bayesian methods and the need for them as you push the forefronts. Lutz-Kelker bias and the influence of pri- ors.

Example: We “know” from supernovae observations that the cosmic expansion is accelerating; the course looks at what this is based on, the assumptions and the uncertainties – which may surprise you.

Probes of the Universe: Black-body radiation (stars and cosmic microwave background (CMB)), brightness temperature. Radio and X-ray Bremsstrahlung. Self absorption. Photoionisation, permitted and forbidden UV-optical-IR emission lines. Production of emission and absorption lines across the wavebands. Absorption features in the spectra of high-redshift quasars. Measuring temperatures and densities. Measuring the sizes of objects that are observationally unresolved…

Fundamental requirements and limitations: range of angular scale; spectral resolution and matched filtering; shot noise, Johnson noise, coherent and incoherent addition, sensitivity; systematics.

Example: The detection of planets outside the solar system – astrometry, radial velocities, eclipses, and their biases.

Astronomical measurement techniques: Traditional collectors. Interferometry: coupling to angular scales, resolving out, sensitivity, clever removal of many systematics, coherence length and path compensation. Following the electric field of the incident radiation versus photon counting. Sky noise, instrument noise, and the hidden problem of surface brightness. Charge coupled devices.

Example: Imaging the CMB – pros and cons of interferometric methods, confusing foregrounds, handling of systematics, the Sunyaev-Zel’dovich effect and its distance independence. The effect of the atmosphere: The atmosphere causes high-resolution images in both optical and radio (for different reasons) to jiggle about, limiting sensitivity as well as resolution. The course considers these phase effects and ways that, without going into space, can overcome them.

Example 1: Adaptive optics – methods of wavefront sensing, design of optimum systems.

Example 2: Optical interferometry – the direct imaging of stars and nearby active galactic nuclei de- spite the jiggling phase.

Part III Physics – Minor Topics 105 BOOKS

Most of the material hasn’t entered textbooks yet, and certainly no book covers the course. The course is therefore designed to be stand-alone, but references are given in the course where useful.

106 Part III Physics – Minor Topics QUANTUM INFORMATION

C H W Barnes

There are no prerequisites for this course. It is a set of new concepts that people who have taken the IB quantum mechanics course could easily step into. You should expect your understanding of quantum mechanics to be challenged.

Introduction: The postulates of quantum mechanics - the Copenhagen Interpretation. Quantum entanglement. Density matrices.

Measurement 1: What constitutes a measurement? Schrödinger’s cat and Wigner’s friend. The Ein- stein-Podolsky -Rosen paradox.

Some alternative interpretations of quantum mechanics: Many worlds. Bohm’s guiding waves. Transaction interpretation. Histories. Quantum-state diffusion.

Hidden variables theories: Bell’s theorem; experimental tests.

Quantum Entanglement: Bipartite systems: Schmidt decomposition, reduced density matrix, entanglement measures. Tripartite systems.

Measurement 2: Positive Operator Value Measure (POVM); Weak measurements.

Decoherence: Decoherence time.

Quantum cryptography: The BB84 protocol. The no-cloning theorem. Eavesdropping strategies. Privacy amplification. Other protocols. Experimental realisations.

Quantum teleportation: Theoretical strategy and experimental realisations.

Quantum computing: Qubits. Logical operations. Algorithms for quantum computers: factorisa- tion, database searches. Error correction. Possible systems for implementing quantum computing: ion traps; nuclear magnetic resonance; semiconductor quantum dots.

BOOKS

An easy to understand introduction to the subject can be found in the March 1998 edition of Physics World and articles on quantum information often appear in the news media.

The following books provide detailed coverage of parts of the course:

Quantum Computation & Quantum Information, Nielson MA & Chuang IL (CUP 2000) The Physics of Quantum Information, Bouwmeester R, Ekart A, Zeilinger A (Spring 2000) Introduction to Quantum Computation and Information, H.-K. Lo, S. Popescu and T. Spiller (World Scientific 1998). Note that this book may not be routinely stocked in bookshops and may have to be ordered. Quantum Mechanics, Rae A I M (3rd edn IOP 1992). The Interpretation of Quantum Mechanics, Onnes R (Princeton 1994). Quantum Theory: Concepts and Methods, A. Peres (Kluwer 1993). There are some very good resources on the World Wide Web such as at: http://www.theory.caltech.edu/~preskill/ph229 - Lecture notes and examples for a course on Quan- tum Information taught by John Preskill at Caltech. Note however that this treatment is much more mathematical than the present course. http://www.qubit.org - The Quantum Information Research Group in Oxford. http://www.cam.qubit.org - The Quantum Information Research Group in Cambridge.

Part III Physics – Minor Topics 107

ADVANCED QUANTUM FIELD THEORY

D B Skinner (Part III Maths)

This course is only suitable for students whose mathematics is very strong. Physics students taking this course may need to do some supplementary reading on Lie group theory, for which the following are recommended:

G. 't Hooft, Lectures on Lie Groups in Physics (given at the University of Utrecht, 2007), available at http://www.phys.uu.nl/~thooft/lectures/lieg07.pdf For more advanced topics: Symmetries, Lie Algebras and Representations, Fuchs J and Schweigert C, (C.U.P 1997), available in the Rayleigh Library.

Quantum field theory (QFT) is the basic theoretical framework for describing elementary particles and their interactions (excluding gravity) and is essential in the understanding of string theory. It is also used in many other areas of physics including condensed matter physics, astrophysics, nuclear physics and cosmology. The Standard Model, which describes the basic interactions of particle physics, is a particular type of QFT known as a gauge theory. Gauge theories are invariant under symmetry transformations defined at each point in spacetime which form Lie Group under composition. To quantise a gauge theory, it is necessary to eliminate non-physical degrees of freedom and this requires additional theoretical tools beyond those developed in the introductory quantum field theory course.

A variety of new concepts and methods are first introduced in the simpler context of scalar field theory. The functional integral approach provides a formal non-perturbative definition of any QFT which also reproduces the usual Feynman rules. The course discusses in a systematic fashion the treatment of the divergences which arise in perturbative calculations. The need for regularisation in QFT is explained, and the utility of dimensional regularisation in particular is emphasised. It is shown how renormalisation introduces an arbitrary mass scale and renormalisation group equations which reflect this arbitrariness are derived. Various physical implications are then discussed.

The rest of the course is concerned specifically with gauge theories. The peculiar difficulties of quantising gauge fields are considered, before showing how these can be overcome using the functional integral approach in conjunction with ghost fields and BRST symmetry. A renormalisation group analysis reveals that the coupling constant of a quantum gauge theory can become effectively small at high energies. This is the phenomenon of asymptotic freedom, which is crucial for the understanding of QCD: the gauge theory of the strong interactions. It is then possible to perform perturbative calculations which may be compared with experiment. Further properties of gauge theories are discussed, including the possibility that a classical symmetry may be broken by quantum effects, and how these can be analysed in perturbation theory. Such anomalies have important implications for the way in which gauge particles and fermions interact in the Standard Model.

BOOKS

An Introduction to Quantum Field Theory, Peskin M E and Schroeder D V (Addison-Wesley 1996) Quantum Theory of Fields, Vols. 1 & 2, Weinberg S (CUP 1996)

108 Part III Physics – Minor Topics NUCLEAR POWER ENGINEERING

G T Parks and R L Skelton

This course is module 4M16 (formerly 4A1) in the Engineering Tripos. It is open to third or fourth year Engineering students and students doing some MPhil courses, for instance the MPhil in Technology Policy, as well as Part III Physics students. There are no hard prerequisites in terms of background knowledge, but familiarity with basic nuclear physics and heat transfer is certainly helpful, and students who cannot solve second-order ordinary and partial linear differential equations will not enjoy parts of the course very much.

This module aims to give the student an introduction to and appreciation of the UK nuclear industry, particularly the technology used in the production of electricity in nuclear power stations, the preparation and subsequent treatment of the fuel and its by-products, and the detection of ionising radiation and the protection of workers within the nuclear industry and the general public from it.

On completion of the module students should:  Appreciate the nature of neutron-nucleus interactions;  Be able to classify ionising radiation by physical nature and health hazard;  Be able to conduct safely a simple experiment involving radiation;  Understand the principles of radiation detection and shielding;  Be able to explain the principles of operation of UK nuclear reactors;  Be able to apply elementary models of neutron behaviour in reactors;  Know how to compute simple power distributions in reactors;  Know how to compute simple temperature distributions in reactors and appreciate their consequences;  Appreciate the significance of delayed neutrons and Xenon-135 to the control and operation of reactors;  Appreciate the advantages and disadvantages of on-load and off-load refuelling;  Be able to perform simple calculations to predict the refuelling requirements of reactors;  Be able to explain the operation of enrichment plant;  Appreciate the problems of radioactive waste management;  Appreciate the range of activities of the UK nuclear industry.

The course consists of 12 lectures, two within-lecture laboratory demonstrations and two examples classes.

LECTURE SYLLABUS

Health Physics: Principles of nuclear reactions; Radioactivity and the effects of ionising radiation; Introduction to health physics and shielding.

Reactor Physics: The fission chain process; Interactions of neutrons with matter; Models for neutron distributions in space and energy.

Reactor Design and Operation: Simple reactor design; Past, present and future reactor designs and concepts; Heat transfer and temperature distributions in commercial reactors; Time-dependent aspects of reactor operations; delayed neutrons and Xenon poisoning; In-core and out-of-core fuel cycles.

Fuel Processing: Enrichment and reprocessing; The containment and disposal of radioactive wastes.

LABORATORY DEMONSTRATIONS

Part III Physics – Minor Topics 109

Demonstration of the use of Geiger-Muller and scintillation counters for detecting ionising radiation.

Demonstration of the detection and shielding of fast and thermal neutrons using a 37 GBq Americium- Beryllium source.

BOOKS

Elements of Nuclear Power, Bennet D J and Thomson J R (Longman 1989) Nuclear Reactor Engineering Volumes 1 and 2, Glasstone S and Sesonske A (Chapman and Hall 1991) Principles of Nuclear Science and Engineering, Harms A A (RSP/Wiley 1987) Introduction to Radiation Protection, Martin A and Harbison S A (Chapman and Hall 1996) Nuclear Chemical Engineering, Benedict M, Pigford T H and Levi H W (McGraw-Hill 1981)

110 Part III Physics – Minor Topics INTERDISCIPLINARY TOPICS – NST PART III

Various departments

Within Part III of the NST, certain courses in the Lent Term, typically of 12 or 16 lectures, are made available across the Tripos, rather than just to one subject within it. These Interdisciplinary Courses are examined in a separate papers in the main examination period at the end of Easter Term.

At present there are three interdisciplinary topics, all on an environmental theme. Students taking Part III PHYSICS may take any of these, each in place of one Minor Topic.

MATERIALS, ELECTRONICS AND RENEWABLE ENERGY Prof. NC Greenham

This interdisciplinary course looks at the physical issues concerning energy generation, storage and use. The style will be varied – making use of simple physical estimates for a wide range of energy problems, but also looking in more detail at materials-based approaches to renewable energy. Only IA-level physics is a prerequisite; those who have experience of solid-state physics will find some parts of the course more straightforward, but the material will be taught and examined in such a way that prior knowledge in this area is not required.

This course is given by the Department of Physics.

For more details, see the separate synopsis on page 112.

CLIMATE CHANGE Prof. D Hodell and others

This course is given by the Department of Earth Sciences and the Department of Geography.

More details will be made available at www.phy.cam.ac.uk/teaching/IDP.php when they are known.

ATMOSPHERIC CHEMISTRY AND GLOBAL CHANGE Dr N Harris and others

This course looks at global change from the perspective of atmospheric composition and its linkage to the climate system. Issues covered include the fundamental photochemical and dynamical processes which control atmospheric composition and structure, and how they would differ in a modified climate. The course is designed to complement the material covered in Course I2 (The Earth system and Climate Change) although either course can be taken independently. The course will be lectured and examined in a way which assumes no prior knowledge for those taking the course.

This course is given by the Department of Chemistry.

More details will be made available at www.phy.cam.ac.uk/teaching/IDP.php when they are known

Part III Physics – Minor Topics 111 MATERIALS, ELECTRONICS AND RENEWABLE ENERGY

N C Greenham

Interdisciplinary Course within Part III of the Natural Sciences Tripos This course is given by the Department of Physics

This interdisciplinary course looks at the physical issues concerning energy generation, storage and use. The course aims to develop skills in using simple physical estimates for a wide range of energy problems, while also looking in more detail at materials-based approaches to renewable energy. Only IA-level physics is a prerequisite; those who have experience of solid-state physics will find some parts of the course more straightforward, but the material will be taught and examined in such a way that prior knowledge in this area is not required.

Energy requirements and energy availability: Back-of-envelope models of energy consumption and production. Current and projected usage. Alternatives to fossil fuels: nuclear, wind, wave, tide, geothermal, solar.

Hydrogen and batteries: Hydrogen vs. electric vehicles. Generation and storage of hydrogen. Elec- trochemical principles. Batteries. Fuel cells.

Exergy: Heat engines, heat pumps. Exergy and exergy efficiency.

Heating and cooling: Practical heat pumps. Combined heat and power.

Engines: The Otto cycle. Stirling engines.

Solar energy: Sunlight, solar concentration, solar thermal. Scale of solar installations required. Theoretical limits to conversion of solar energy.

Electronic structure of molecules and solids: Tight-binding band structure. Interaction with light. Excitons. Electrons and holes. Doping.

Inorganic semiconductor solar cells: The p-n junction. Photovoltaic operation. Cell design, materials and performance.

Molecular semiconductors: Materials and optical properties. Excitons. Marcus theory. Photo- voltaic devices: multilayers, bulk heterojunctions and dye-sensitised cells.

Advanced photovoltaics: Tandem cells. Multiple exciton generation.

Photosynthesis: Structure and optoelectronic operation. Charge separation and recombination. Ef- ficiency. Biofuels.

BOOKS

Sustainable Energy - Without the Hot Air, Mackay D J C (UIT Cambridge 2009) The Physics of Solar Cells, Nelson J (Imperial 2003) Molecular Mechanisms of Photosynthesis, Blankenship R E (Blackwell 2002)

112 Part III Physics – Minor Topics ENTREPRENEURSHIP

S Barakat

Overview

ETECH Projects is best suited for students who see themselves as would-be entrepreneurs or as those who expect to work in situations where they will have to assess ideas, technologies or propositions for their commercial viability. ETECH Projects has come a long way since its origins in 2001. Since then ETECH Projects has grown to reach out to more university departments, and more than 600 students have gone through the course and almost 50 inventors have been supported. The course is offered every year in the Lent term primarily to students from Chemical engineering, Material Science, Biological Sciences and Physics. ETECH Projects allows students interested in entrepreneurship to work closely with inventors developing cutting-edge science and technology. The students work as a team to evaluate the commercial potential of novel, potentially disruptive technologies. In many instances the teams are multidiscipli- nary, offering further insights into how a disruptive technology is viewed from different perspectives. The blend of skills developed through the course are needed in a variety of contexts from early stage companies, venture capital, corporate venturing and technology transfer environments. By assessing commercial due diligence of novel technologies, ETECH Projects helps students develop key entrepre- neurial skills such as opportunity recognition and evaluation in the context of science-based entrepreneurship.

Please see more on http://www.cfel.jbs.cam.ac.uk/programmes/etech/index.html

ETECH Projects objectives • Assessment of market potential and viability of novel technology based concepts • Build skills to carry out due diligence on the emerging technology. • Perform practical group work to apply these skills to new business ideas. • Work in a multi-disciplinary setting on projects.

Lectures Twelve 1-hour sessions will cover the key elements of successful commercialisation of novel, emerging technologies. There will be practitioner-delivered guest lecturers supplementing the lecture/discussions to be led by the faculty. The guest lectures will be delivered by invited local entrepreneurs and investors providing practical insights that come from experience gained in Europe’s top technology cluster.

Topics covered will include the key aspects of commercialisation as follows:

Commercialisation aspect Key topics Technology Attributes, IP position Application Viability, Linking technical and commercial advantages Market and Industry Target markets, Size and growth rates Competitors/Partners Current/future competition, Potential partners Business Model Potential business models, Pros and cons Recommendations Target market, Most suitable business model Next Steps Immediate next steps to commercialisation

Tutor Supervisions

Part III Physics – Minor Topics 113 Each student team will prepare a commercial feasibility report and present the findings to the inventor(s). Students will be provided with supervision support during the course of the commercial due- diligence process. The supervisions will be structured according to the requirements of each ‘ETECH Project’, but will broadly cover opportunity evaluation, developing the business concept and presenting the findings. A sample supervision guidance sheet is enclosed in Appendix B.

Readings and Supporting Material Students will be provided with a comprehensive course pack that includes a course handbook and providing much of the background material required for the commercial assessment. Reading lists will be provided at the start of the course and at different points during the term that students can draw on to deliver assignments and supplement the lecture notes. Lecture slides along with additional materials are posted on Camtools. Students wishing to gain further insights into the field before the class should read the following texts, both of which are excellent: New Venture Creation, Timmons J A and Spinelli S (6th edn Irwin McGraw Hill 2004) The High-Tech Entrepreneur’s Handbook, Lang J and the Cambridge University Entrepreneurship Centre (Pearson Education 2001)

Assessment The course will be assessed by two sets of coursework, which are designed to test candidates’ ability to apply the concepts, tools and techniques covered in the syllabus. Similar tasks are regularly performed by entrepreneurs and investors and are important steps in developing the self-efficacy and compe- tence of those who take the course. One set of the assessed coursework is made up of individual pieces of work and the other is the group project mentioned above, working with an inventor and evaluating the commercial potential of a real invention. Full details are in the course handbook distributed in class.

114 Part III Physics – Minor Topics ETHICS IN PHYSICS

R Jennings

This course of four workshops will address ethical issues that arise in doing physics. The format will be a moderated discussion of ethical problems that arise in four areas as follows:

Workshop 1 – military research Workshop 2 – the politics of science and government funding policy Workshop 3 – the use and abuse of data Workshop 4 – intellectual property and allocation of credit

Broadly speaking the first two workshops are concerned with the responsible conduct of research and the second two with the applications of physics. My intention is to run a fairly open plan course, and I am willing to introduce topics of particular interest to participants. That said, the default topics are as follows:

Workshop 1 For this first ethics in physics workshop I will introduce some of the ethical questions that arise in doing military research and indicate alternatives to military research. My main resources are pub- lications of Scientists for Global Responsibility. Three in particular are of interest and are available as handouts on the TIS:

Soldiers in the Laboratory More Soldiers in the Laboratory Behind Closed Doors

Workshop 2

This workshop will look at the politics of science and the origins of the government's funding policy. The discussion will focus on the question of how to balance the funding of pure basic research with the government’s priority for wealth creation. This is a particularly sensitive issue for the most basic fields of research such as particle physics and astronomy. The issues arise in a classic debate in the Journal Minerva Volume 1, 1962: Michael Polanyi, “The Republic of Science: Its Political and Economic Theory” pp. 54-73. Alvin Weinberg, “Criteria for Scientific Choice” pp. 159-171.

Workshop 3

To compare Robert Millikan’s dubious presentation of data in his 1913 paper, "On the elementary Electrical Charge and the Avogadro Constant," [The Physical Review Series II, Volume II, No. 2, (1913), pp. 109-143] and the more notorious presentation of data by Jan Hendrick Schön. The Millikan case is available at: http://www.onlineethics.org/Education/precollege/scienceclass/sectone/cs2.aspx

Workshop 4

Problems of intellectual property range from straightforward plagiarism to industrial espionage. At a more subtle level, there are problems of how credit is shared out among members of a group working on a research project. We will discuss two cases: the case of Rosalind Franklin and her contribution to our knowledge of the chemical structure of DNA, and the case of Jocelyn Bell Burnell and the discovery of pulsars. In each case there is still a range of opinions concerning the distribution of credit, and these two cases provide good examples of the difficulties that can be en- countered in fairly sharing the credit for discoveries. The case of Rosalind Franklin is available at: http://www.onlineethics.org/Education/precollege/scienceclass/sectone/cs4.aspx

Part III Physics – Non-examinable courses 115 PHILOSOPHY OF PHYSICS

J Butterfield

This course of four lectures offers an introduction to the philosophy of modern physics. This is a technical area, although an interdisciplinary one. Its closest cousin is the branch of physics called ‘foundations of physics’. Thus in both areas, we examine the mathematical structures of physical theories. This course will emphasise two specific theories: relativity and quantum theory.

The first and second lectures will survey the philosophy of relativity theory. I will emphasise Einstein’s fa- mous ‘hole argument’, as a lesson about the foundations of general relativity. Einstein devised this argument in late 1913, as an argument against general covariance: namely, that any generally covariant theory would be radically indeterministic. Late in 1915, after he had found the field equations of general relativity, which are generally covariant, he re-assessed the argument as showing only that we should not think of spacetime points as objects, on pain of a radical indeterminism. Broadly speaking, there the matter rested, until about twenty years ago, when the assessment of the argument became again a live topic, because of its connection with other issues in the interpretation of general relativity. The controversy continues today.

The third and fourth lectures are devoted to the measurement problem of quantum theory: in short, Schroedinger’s cat. There are many aspects, technical and philosophical (and even historical), one could discuss about this. I will in part be guided by the interests of the class. But here are two:

(i) The nature and role of decoherence. In short, decoherence gives a dynamical basis to the selection of a preferred quantity, but does nothing to ‘select’ an individual, definite measurement-outcome, or more generally a definite macroscopic reality.

(ii) The current prospects for the Everett interpretation (also known as: the relative-state, or many worlds, interpretation). In short, the interpretation is very strange, but its current prospects are surprisingly good!

BOOKS NB: Most of the books cited will surely be in your College library.

All four Lectures: The Stanford Encyclopedia of Philosophy (SEP), and the Pittsburgh philosophy of science e-arXive, both available online, have many good philosophy of physics articles. First and second Lectures: Theoretical Concepts in Physics, Longair M, (2nd edn CUP 2003); Chapter 17.1-2. SEP article on Einstein’s philosophy of science: http://www.seop.leeds.ac.uk/entries/einstein-philscience/ SEP article on Einstein’s Hole Argument http://www.seop.leeds.ac.uk/entries/spacetime-holearg/ Third and fourth Lectures: Speakable and Unspeakable in Quantum Mechanics, Bell J S (2nd edn CUP 2004); Chapters 20 and 23 Philosophical Concepts in Physics, Cushing J T (2nd edn CUP 1998); Chapters 20-22. SEP article on Bell’s theorem: http://www.seop.leeds.ac.uk/entries/bell-theorem/ SEP article on decoherence in quantum mechanics: http://www.seop.leeds.ac.uk/entries/qm-decoherence/ Pittsburgh e-arXive articles on the Everett interpretation include the following two: philsci-archive.pitt.edu/archive/00000208/ and philsci-archive.pitt.edu/archive/00000681/

Students doing Part III Physics are welcome to attend the weekly non-examinable seminar in Philosophy of Physics given in Mathematics, in both Michaelmas and Lent Terms. In 2012-2012, the details are: Thursday s at 4.30, weeks 1 to 8, Michaelmas and Lent Term, Meeting Room 13 in CMS

116 Part III Physics – Non-examinable courses PROJECTS

C G Smith

Please note that from 2014-15 the project allocation procedure with be changing.

Each Part III Physics student is required to undertake a project worth about one-third of the final tripos mark. A project is aimed at investigating a topic of current interest in physics, giving an opportunity for original work and ideas. The precise form of the project may vary from topic to topic and will be specified by the supervisor.

The various types of project work available are as follows:

Experimental Project: generally this is an extended investigation, which is open-ended and gives considerable freedom of approach.

Theoretical Project: this is a small-scale theoretical research project, requiring an element of original theoretical development and/or computation.

Computing Project: this generally requires the writing or use of computer programs to investigate some aspect of physics. Some theoretical work is usually required as a basis for the program.

The project abstracts, provided by members of staff and Senior Research workers, are available on the web: see (http://www-teach.phy.cam.ac.uk/pt3projects/ for a direct link to the project pages). Students may also suggest projects of their own, but they must have a supervisor (who may be external) and the project must be approved in advance by Professor Smith. Students interested in a particular project should discuss it as soon as possible with the relevant supervisor. The list of projects on the web will be continuously updated to show which ones have already been taken.

Students must choose their projects by the end of the fourth week of Michaelmas term. Supervisors will decide, by that same deadline, which students may undertake their projects, but they are asked not to make a decision until Thursday, October 24th 2013, at the earliest. The purpose of this delay is to allow students time to talk to several supervisors and to allow supervisors to find the most suitable students for their projects. In response to student concerns, a code of practice for projects allocations has been agreed by both the Teaching Committee and the Staff Student Consultative Committee – see below for the full version.

Supervisors will offer the project to a student using the web interface, where they will also indicate the safety risks associated with the project, and students will be asked to indicate their acceptance of the offer, via email. In the interests of fairness both to the supervisor and to fellow students, students will not normally be allowed to change their project once they have accepted an offer.

Safety

In all research there are possible risks associated with performing the work. Each supervisor will indicate what the risks are associated with their experiment on the sign up form. Before the project starts the student and supervisor will sign a project card which will confirm that the student will be trained appropriately to cover the risks associated with the project. No project will start until this card is received in the Teaching Of- fice. The card will also list the name of the “day to day” supervisor and the laboratories in which the student will be working. If there is a safety hazard associated with the project then supervisors will suggest appropriate safety courses for the student to go on. The laboratory will provide these safety courses, which will be held in the Michaelmas term. Attendance records will be taken at these lectures and no student will be allowed to start their project unless they have attended the appropriate courses. Supervisors and Students will now complete and sign a risk assessment form showing they understand the risks associated with their project experiments. These forms will be prepared with the help of the supervisor and these will be handed in to the Teaching Office before the start of experiments or before Friday, December 6th 2013, whichever

Part II Physics – Projects 117 is the sooner. They will then be passed on to the Safety officer. Changes of experimental procedure during the project will require an updating of the risk assessment forms.

Where work is performed in Laboratories outside the Cavendish Laboratory, the Teaching Office will write to the department concerned drawing attention to the fact that one of our students will be working there to get their agreement on the project going ahead. If for any reason a project needs to move between departments the Teaching Office must be informed and the new department made aware of the arrangements.

Expected time students should spend on the project

The project workload is expected to take up one third of your time for the year:

Michaelmas Term: approximately one sixth of your project time spread through the term.

Lent Term: approximately four sixth of your time with concentrated effort at the beginning and end of the term.

Easter Term: one sixth of your project work, at the beginning of Full Term.

Students should not devote too much time to the project to the detriment of their preparation for the examinations. Students should schedule their time carefully, and start as early as possible, so as not to conflict with preparation for exams during the vacations.

Laboratory Note Book

Students will be required to keep a laboratory note book during the project. This will act as a day to day record of the project work and will be handed in with the project write up. Although the note book will not be marked, the information in it will be used in assessment of the project and will help indicate how the day to day issues that come up in the research were dealt with. During the safety course there will be a presentation on what is expected in the Laboratory note book.

Progress reports

Students will be asked to complete two progress reports. At the end of the Michaelmas Term you should submit a Project Plan (one copy; approximately 500 words) which would normally include a statement that the relevant literature has been consulted. This should be signed by your supervisor to indicate his or her agreement with the plan and should be handed in by Friday, December 6th 2013. The signed copy of the Project Plan will be retained by the teaching office and forwarded to the assessor in Easter Term – failure to submit a project plan will result in the loss of 5% of the available project marks. The second report is a simple “tick box” form, which will be issued during week 6 of the Lent term. This will invite you to report any problems with your project, and to confirm that a presentation has been scheduled. The second report will not form part of any assessment, but will allow any problems to be identified by Professor Smith well before the time the project has to be handed in.

It is very important that students bring any unforeseen delays or other problems with their projects to Pro- fessor Smith’s attention at the earliest possible opportunity. The earlier such problems are addressed, the more chance there is of taking suitable remedial action.

Supervisions and presentation

Supervisors should offer up to six supervisions on the project. One of these should be in the form of a presentation of preliminary project results; either to the supervisor’s research group (strongly encouraged) or to a small group of say 4 — 6 project students and supervisors. It is expected that supervisors will organise these presentations in about the seventh week of the Lent term, (or later, perhaps even at the very start of the Easter term, if mutually acceptable). Students will receive feedback on the content and presentation of their projects from the supervisors and others present, which should help them with their oral exam. This form of

118 Part II Physics – Projects presentation is aimed at developing communication and presentational skills. Failure to give this presentation will result in the loss of 5% of the available marks for the project.

The formal write-up

The project should usually be presented in the style of a paper published in a scientific journal. The style of the project should be agreed with the supervisor. The main text (excluding appendices and abstract) should be concise (20–30 pages, 5000 words maximum). The text should describe and explain the main features of the project, the methods used, results, discussion and conclusions. Detailed measurement records, calculations, programs, etc. should be included as appendices. (Programs of more than a few hundred lines can be submitted – one copy only – flash stick or, preferably, CDROM: please ensure it is labelled with your Examination number.) In addition, there must be an abstract of at most 500 words.

The student and supervisor should discuss the general structure of the report before writing is started, but the supervisor should not read a full draft before submission. A set of handy tips and information is given in the booklet entitled Keeping Laboratory Notes and Writing Formal Reports, which is handed out to students at the start of the year and is also available on the web - make sure you get one.

Submission of the project

The deadline for submission of the project is:

4.00 pm on the third Monday of Easter Full Term (12th May 2014).

An request for a delay in the hand-in date of your project report due to illness must go through your Director of Studies and then be agreed by the Applications Committee. Treat this deadline like you would an exam date. Two copies of the project plus your laboratory note book should be handed in to the Teaching Office (Room 212B, Bragg Building) in person before the submission deadline. In order to preserve anonymity when your project is looked at by the Part III examiners, your name must not appear on the project itself. Two cover sheets, available from the Teaching Office, should be attached to the front of each project. The blue cover sheet, which has a space for both your name and candidate number, goes on the outside. The green cover sheet, which has only your candidate number, goes immediately behind it. (The blue sheet will be removed before the Part III Examiners receive your report). You should ensure that your candidate number appears on the first page of your project, together with the title of the project and your supervisor’s name. The blue cover sheet contains the following declaration, which you should sign: Except where specific reference is made to the work of others, this work is original and has not been already submitted either wholly or in part to satisfy any degree requirement at this or any other university.

Project Assessment

As soon as possible after submission, the project will be assessed by two people, normally the supervisor and another staff member (the assessor), who will conduct an informal oral examination of the student on the work. The assessor, who will be appointed by the Teaching Committee, will not usually be a specialist in the field. The student will be asked to present a short verbal summary, normally uninterrupted, of the project during the interview. A projector will be made available if requested in advance. Students should expect to be contacted by their supervisor shortly after handing their project in, to arrange the oral examination.

The supervisor and assessor will write separate reports plus a joint report to the Part III Examiners and will recommend a mark. These marks are not necessarily final and may be amended by the examiners, who also look at the projects.

Part II Physics – Projects 119 The following guidelines for allocation of marks to Part III Projects will be given to assessors. Each heading carries equal weight.  Scientific content: How much appropriate understanding of science (particularly physics) was shown?  Quality of work: How carefully/accurately/successfully was the work planned and performed (the laboratory note book will be used to help assess this). Was an appropriate amount of relevant material included?  Communication skills: Report: was the report well written and clearly organised, with clear and well-balanced arguments, appropriate use of figures and tables, etc? Viva: was the student able to summarise the work and to respond coherently to questions?

After the oral examination, the assessors will return their report and recommended marks, along with both (signed) copies of the projects and the Laboratory note books, to the Teaching Office (Room 212B, Bragg Building). After publication of the Part III Class List, students may, if they wish, retrieve one copy of their project from the Teaching Office.

If there are any questions about these arrangements come and see Professor Smith, in the Mott Building, Room 358, telephone 37483, e-mail [email protected].

Further information:

Allocation of Projects

In response to concerns about the transparency of the project allocation process, the following text has been approved by the Teaching Committee and the Staff Student Consultative Committee. Project supervisors are enjoined to act within the spirit of the following code.

Code of Practice for allocation of Part III Projects Part III Projects cover the full range of research in Physics, involving analytical, experimental and computational work in various proportions. They may involve working in research groups either in the Department of Physics or elsewhere in the University. Part III projects are often closely linked to the supervisor’s own research, and may result in single or joint publication. Unlike Part II Research Reviews, the successful conclusion of a project requires a reasonable match between the skills and interests of the student and those required by the project. It is reasonable that the project supervisor should be the judge of these: it is not therefore appropriate to assign projects by a general lottery, for example.

Supervisors are, however, asked to ensure fair play in the allocation process. This requires that the requisite skills be fully advertised in the project abstract, and that the supervisor should be prepared to discuss the project with all students who make serious inquiries. He or she should also keep an open mind until the end of the consultation period, and should then make and announce a decision as quickly as possible, to avoid keeping students “on a string”. If more than one student indicates serious interest, the supervisor should make clear how he or she in- tends to make the allocation – in some cases this might be as simple as drawing names from a hat, while for an analytical project closely tied to the supervisor’s research project, it might be on the basis of performance in TP1 and/or TP2 in the previous year. The essential point is that whatever method is used should be seen to be appropriate and fair, should be clear to the students, and should be settled expeditiously once the system opens to allocations. Students can then make a reasonable guess at their chances, and can pursue such other projects as they wish.

Supervisors may create projects expressly for a particular student, and are encouraged to do so (either in response to the student’s initiative in proposing the project, or in response to strong demand). However, such projects should not be advertised to the class via the web, but should be

120 Part II Physics – Projects flagged as “hidden” or “inactive” until allocated. As well as not raising false hopes, this will also avoid having to answer unwanted inquiries.

Out of fairness to supervisors, students are not normally allowed to change projects once they have been allocated one and have accepted it. This places an additional responsibility on supervisors to ensure a fair, transparent and efficient allocation.

Further Health and Safety considerations

Supervisors should always discuss safety aspects of their projects with the students concerned, mentioning potential hazards and procedures with which students may not be familiar. Supervisors should ensure that the student has read and understood the relevant risk assessments for the activities to be carried out. For new activities, risk assessments should be carried out by the supervisor in consultation with the student. For safety reasons, students must at all times remain within shouting distance of help, and, if performing an experiment, sign in a book provided by the supervisor, on each occasion when they start and when they finish work. They are only allowed to work on experiments in the Department outside normal lab hours in excep- tional circumstances, by prior arrangement with the supervisor, and with the approval of the Departmental Safety Officer and the Head of Department. Supervisors must ensure that students are aware of general and experiment-related emergency procedures. By accepting the project, students are indicating their agreement to abide by these and other safety rules.

Use of bibliographic databases

The Web of Science database (http://wok.mimas.ac.uk) may be used to find relevant papers. Students must first sign a form (available from the Rayleigh Library) unless they signed one last year

Part II Physics – Projects 121 122

Guide for Students

Guide for Students 123

Academic Staff Staff member Telephone Room Group E-mail (sec’y) Alexander, Prof. P 37477(37294) G24 AP [email protected] Allison, Dr W 37416(37336) 413B SMF [email protected] Ansorge, Dr R E 66103 240 BSS [email protected] Atatüre, Dr M 66465(66298) 982 AMOP [email protected] Barnes, Dr C H W 37487 361 TFM [email protected] Batley, Dr J R 37434(37227) 953 HEP [email protected] Baumberg, Prof. J J 37313 24 IRC OE [email protected] Bohndiek, Dr S T.B.A. T.B.A. BSS [email protected] Buscher Dr D F 37302 G26 AP [email protected] Castelnovo, Dr C 37433 528 TCM [email protected] Cicuta, Dr P 37462 237 BSS [email protected] Cole, Dr J 37470 (37336) 429 SMF [email protected] Cooper, Prof. N R 65127 528 TCM [email protected] Donald, Prof. Dame Athene M 37382(37423) 243 BSS [email protected] Eiser, Dr E 37267 238 BSS [email protected] Ellis, Dr J 37410 427C SMF [email protected] Ford, Prof. C J B 37486(37482) 330 SP [email protected] Friend, Prof. Sir Richard H 37218(37313) 32 IRC OE [email protected] Gibson, Prof. V 37373(37227) 958 HEP [email protected] Green, Dr D A 37305(37294) F30 AP [email protected] Greenham, Prof. N C 66301(37313) 33 IRC OE [email protected] Gripaios, Dr B M 61014 961 HEP [email protected] Grosche, Dr F M 37352 409 QM [email protected] Gull, Prof. S F 37367(37294) F22 AP [email protected] Hadzibabic, Dr Z 37004 835 AMOP [email protected] Haniff, Prof. C A 37307 F29 AP [email protected] Hobson, Prof. M P 39992 F08 AP [email protected] Hughes, Dr H P 37327(37313) M210 OE [email protected] Irvine, Dr A C 37555 M232 ME [email protected] Jardine-Wright Dr L 33318 212A Outreach [email protected] Jones, Dr G A C 37484(37482) 359B SP [email protected] Keyser, Dr U 37272 239 BSS [email protected] Khmelnitskii, Prof. D C 37289(37254) 521 TCM [email protected] Lamacraft, Dr A 37378 529 TCM [email protected] Lasenby, Prof .A N 37293(37294) K28 AP [email protected] Lester, Dr C G 37232 952 HEP [email protected] Longair, Prof. M S 65953 G25 AP [email protected] Maiolino, Prof. R 61661 K35 AP [email protected] Needs, Prof. R J 37384(37254) 535 TCM [email protected] Padman, Dr R 37310(37294) F21 AP [email protected] Parker, Prof. M A 37429 210 Head of [email protected] Depart- [email protected] ment Payne, Prof. M C 37381(37254) 541 TCM [email protected] Phillips, Prof. R T 37342(37313) 874 AMOP [email protected] Queloz, Prof. D P 37083 F24 [email protected] Richer, Dr J S 37246 F28 AP [email protected] Riley, Dr J M 37308 F23 AP [email protected] Ritchie, Prof. D A 37331/37255 361 SP [email protected] Saunders, Dr R D E 37301(37294) F08 AP [email protected]

Guide for Students 125 Simons, Prof. B D 37253(37254) 539 TCM [email protected] Scott, Prof. J F 37391 502 QM [email protected] Sirringhaus, Prof. H 37557 M208 ME [email protected] Smith, Prof. C G 37483(37482) 358 SP [email protected] Steiner, Prof. U 37390 35 IRC BSS [email protected] Terentjev, Prof. E M 37003 245 BSS [email protected] Thomson, Prof. M A 65122/(37227) 951 HEP [email protected] Ward, Prof. D R 37242(37227) 939 HEP [email protected] Warner, Prof. M 37380(37254) 505 TCM [email protected] Withington, Prof. S 37393(37294) 816B AP [email protected]

“M” indicates Microelectronics Building - “IRC” indicates Interdisciplinary Research Centre “B” indicates Battcock Centre

Administration The Department’s central administration is located in the Bragg Building. Enquiries are usually dealt with via Room 206, between 9:00 and 12:30, and 14:00 and 17:00. Aims and Objectives The Quality Assurance Agency, through its institutional audit of the University, is concerned with the assurance of the quality of teaching and learning within the University. The University in turn requires every De- partment to have clear aims and objectives and to monitor their teaching and learning activities and consider changes where necessary, and meet various criteria concerning management of the quality of its teaching provision. Students play a vital role in assisting with this quality assurance, and the Department welcomes constructive comment via the Staff-student Consultative Committee. Appeals Information about the procedure for examination warnings, allowances and appeals is available at http://www.admin.cam.ac.uk/students/studentregistry/exams/undergraduate/exams.html. Astronomical Society (CUAS) Astronomy is a popular branch of physics and the Astronomical Society provides an interesting series of lectures on Wednesday evenings during the Michaelmas and Lent Terms, details of which can be found on the society’s web page - http://www.cam.ac.uk/societies/cuas/. Members of the research groups of the Caven- dish Laboratory concerned with astronomy are often lecturers in this series. Bicycles The Cavendish Laboratory provides several cycle sheds and racks in which you may leave your bike, but it should be locked with a sturdy security device when not in use. Several serious accidents occur every year involving students cycling in Cambridge: please cycle with care, use proper lights when required and wear a safety helmet. Books The Physics Course Handbook lists the most important books to be used in conjunction with the lecture and practical courses. Reading and working through parts of these books are indispensable exercises which are usually considered part of the course. Many of the books are expensive, but they may be obtained at substantial reductions by attending book sales and looking out for bargains listed on College noticeboards and those in the Cavendish. All books recommended for Part I should be available in College libraries or the Rayleigh Library. If you notice any omissions, please fill in a request slip to ensure that the book is ordered. Bookshops The main bookshops from which you should be able to obtain the recommended books are Heffers, CUP and Waterstones. And then there is always Amazon… Note: a 20% discount is available at the CUP bookshop with a University Card.

126 Guide for Students Buildings The present Cavendish Laboratory comprises the extensive buildings south of Madingley Road, the first of which opened in 1973. A map of the Cavendish Laboratory site is shown on the inside back cover. The original buildings on this site were the Rutherford, Bragg and Mott Buildings, named after former Cavendish Pro- fessors, and the workshop building between the Rutherford and Bragg buildings. These have in the past few years been supplemented by a building for the Interdisciplinary Research Centre (IRC) in Superconductivity (now the Kapitza Building), and a further building for the Microelectronics Research Group and Hitachi Cambridge Laboratory. Further recent additions to the site are the Magnetic Resonance Research Centre of the Chemical Engineering Department, the first phase of the Physics of Medicine (POM) building, which houses the laboratories for the Biological and Soft Systems sector (BSS), the Nanoscience Centre and the Terrapin Building. The most recent addition is the Battcock Centre for Astrophysics, which houses the Astro- physics Group and is located on the Institute of Astronomy site off Madingley Road. Calculators When considering which calculator to buy, you may wish to bear in mind that only certain types are permitted for use in Tripos examinations. Among these are the Casio models available from the Cavendish Stores. Calculators will also need the ‘official’ Board of Examination yellow sticker which can be obtained from the Board of Examination offices in Mill Lane. CamCORS The supervision reporting system. See Databases (below) CamSIS The student information system. See Databases (below) CamTools CARET’s Virtual Learning Environment. See Databases (below) Canteen See Common Room (below). Careers The University Careers Service is located in Stuart House, Mill Lane (telephone number 338288), and is fi- nanced by the University to provide students with information about careers and assistance with application processes. The Service maintains an information room which can be used during normal office hours, and additionally provides expert staff to advise students about career-related issues. Ask at the reception desk. Cavendish Laboratory The Cavendish Laboratory is the name of the building which houses (most of) the University’s Department of Physics; the name has become synonymous with the department itself. The laboratory was established through the generosity of William Cavendish, Seventh Duke of Devonshire, who endowed the laboratory in the nineteenth century, together with the Cavendish Chair of Experimental Physics. The original Cavendish Laboratory was located in Free School Lane, and opened in 1874; the Department moved to the present site in 1973-74. The history of the Cavendish is well illustrated in the Cavendish Museum, located in the Bragg Building. Cavendish Stores Next to the Common Room in the Bragg Building is the central “stores” of the whole laboratory, the opening hours of which are 8:00 -16:45. The stores sell past examination papers, the booklet of mathematical formulae, and calculators for examinations. Cheating The Department considers the act of cheating as a serious matter and any incident will be reported to the Head of Department, who will normally refer the case to the University Proctors.

Guide for Students 127

It is unacceptable to:  cheat during oral or written tests  copy the work of others and submit as your own  falsify and/or invent experimental data In the practical classes, some experiments are designed to be carried out individually and some in collabora- tion with other students. Discussion among students and with demonstrators and Heads of Class is encouraged and you may use any help or insights gained in these discussions to improve your experiment, your understanding of the physics and your written report. However, your report should be written by you, following the guidelines on writing reports, and only data collected in your experiment should be presented as your own. The Department has access to the latest anti-plagiarism software tools and will use them from time to time to monitor coursework submissions for plagiarism, and so ensure fairness for all students. Classing Criteria The Department of Physics has agreed that examiners will mark to agreed criteria for written examinations. Due to the way in which marks from different subjects are combined to create the final list in Parts IA and IB, the criteria used in Physics are not reflected directly in the class list. For Parts II and III, the examinations are under the direct control of the Department, in conjunction with scrutiny by External Examiners. The criteria for classing in Physics are available at http://www.phy.cam.ac.uk/teaching/classing.php. College Your College ordinarily admits you to the University, provides you with accommodation and arranges for your supervisions in Parts IA and IB. Usually, but not always, your Director of Studies in Physics will be a member of staff of the Cavendish, and will be directly in touch with the Department. Most Colleges aim to provide supervision at a rate of about one hour per week for each of Part IA Physics, Part IB Physics A and Part IB Physics B. Part II and Part III supervision is provided on behalf of the Colleges through a scheme administered in the Department. Common Room The Cavendish contains a large Common Room which is open to all students of Physics. It is open for light refreshments from 10:30-16:30, and for lunch from 12:30-13:45, on Mondays to Fridays. In addition there is an area for relaxation outside the lecture theatres, where there are vending machines for food and drink. Room 700 on the bridge between the Rutherford and Bragg buildings, above the metal stores is available for private study for Pt II and III students. Complaints If you have a complaint about the teaching or administration in the Department, take it up first, if possible, with the person directly concerned in a constructive manner. If this is not effective, or if the matter seems to be of general interest, you may wish to discuss it with your course representative on the Staff-Student Con- sultative Committee. It may also be useful to discuss the matter with your Director of Studies or Tutor. If your complaint is substantial, by all means take it to the Director of Undergraduate teaching or the Head of Department. There is also a formal University Complaints Procedure, of which you should have received details. If you need advice on whether or how to proceed with a formal complaint, you could ask your College Tutor or Director of Studies, or your CUSU representative, or any physics member of staff. (See also Harass- ment, below.) Computing The Department relies on the University Computing Service for the provision of computing facilities for undergraduates. The Managed Cluster Service (MCS – formally PWF) is located close to the Practical laboratories, where you can use networked PCs with a range of software for word-processing, spreadsheet calculation and dataplotting. Most colleges also provide some facilities.

128 Guide for Students The Department makes increasing use of computers in practical work, and aims to develop specific skills in the use of computers for solving problems in physics. Counselling The University Counselling Service is at 14 Trumpington Street (telephone 332865), and is open 9:00 - 17:30, Monday to Friday. It exists to help members of the University who have problems of a personal or emotional nature which they wish to discuss in confidence. The Service is widely used, so it can be very busy, and it is best to make an appointment either by telephone or in person. In times of particular stress a special effort will be made to see you quickly. Advice on personal matters is always available in your college through your Tutor. Special assistance is provided by Linkline (internal telephone 44444, external line 367575) and the Samari- tans (telephone 364455). Courses The Department of Physics offers a wide range of courses in Physics, at undergraduate and postgraduate level, many of which are detailed in the Lecture List which is available online http://www.phy.cam.ac.uk/teaching/lecture.php from mid-September. Some specialised courses for postgraduate students are not advertised in this way. The detailed synopses of the courses for Tripos are given in this Handbook, which is distributed at the beginning of the academic year to all students taking physics courses. Databases Students taking courses in Physics will come across a number of different on-line databases. Because these all use the same login method (“Raven” authentication: see below), it is not always obvious that these are different systems, which for the most part do not (yet) talk to each other. The four main databases are:  CamCORS – the Cambridge Colleges Online Reporting System. Supervisors use this to report to Directors of Studies and Tutors on the progress of their supervisees, and to claim from the colleges for the supervisions provided. If colleges choose to release the information, students can view their supervision reports here directly. See http://www.camcors.cam.ac.uk/  CamSIS – the student information system. Students use this to enter for exams, and (when the results are uploaded) to check their Tripos results. Part IB NST students also indicate their Part II subject choice through this system. See http://www.camsis.cam.ac.uk/  CamTools – a Virtual Learning Environment (VLE) run by CARET, the Centre for Applied Re- search in Educational Technologies. Most Part IA NST courses have their own pages on Cam- Tools. The Department of Physics uses instead the Teaching information System (TiS; see below) which permits better integration with other Departmental systems. See http://camtools.cam.ac.uk/  The Teaching Information System – a web database system run by the Department of Physics. All course resources are provided here. It is important that all students register directly with the TiS each year, in addition to entering for examinations on CamSIS. (see Registration: below). See http://www-teach.phy.cam.ac.uk Department of Physics The Department of Physics is the administrative unit in the Faculty of Physics and Chemistry which provides teaching in physics leading to the Part II and Part III examinations in Physics. The Head of Department is Professor Andy Parker. Your direct contact with the Department can be through your College (your Director of Studies in the first instance) or through the staff you encounter in lectures and practicals. The needs of students in Part I are usually met fully through College contacts; in later years direct contact with the De- partment increases. Notices are posted near the lecture theatres and practical classes which all students should read, since this is where details of examination procedures are advertised. The Department provides various facilities specifically to help you in your study of physics, many of which are described in this document.

Guide for Students 129 Director of Studies You will have been assigned a Director of Studies in your College - possibly one for Physics and another for Natural Sciences overall. This person will assign you to supervisors during your first two years, will monitor your progress and try to assist you if you have problems. If you get into difficulties with the course you should discuss this with your Director of Studies, or with your Tutor. If for any reason you feel unable to do this any member of staff of the Department will willingly try to assist you. Disability The Department is happy to cater for the needs of students with disabilities. Students with disabilities which require special arrangements to be made should contact the Teaching Office in good time. Electronic Mail Electronic mail is widely used as a good way to communicate with your supervisors, and also provides the mechanism for offering comments on the courses offered by the Physics Department (see Year Groups). It is also used by the department to contact students. Examinations The marks upon which your degree classification is based are derived from a combination of continuously- assessed work, set pieces (such as projects) and examination papers. There is one three-hour paper in Phys- ics for Part IA, two for Part IB Physics A, two for Part IB Physics B, and seven or eight two hour papers for Part II. In Part III most examinations are taken at the beginning of the term following that in which the course is taken; there is a 3-hour paper in General Physics at the end of Easter term. See Natural Sciences Tripos http://www.cam.ac.uk/about/natscitripos/exams/ and Classing Criteria http://ww.phy.cam.ac.uk/teaching/classing.php for details of the grades that may be obtained. Preparation for examinations is important, and the best method to use varies widely between individuals. The Physics Department has produced some guidance which you might find helpful and is available on the teaching pages on the web at http://www.phy.cam.ac.uk/teaching/exam_skills.php. If you have problems it is worth discussing them with your supervisor, Director of Studies or your Tutor, who may be able to assist by suggesting alternative approaches. Information on the various styles of questions is available at http://www.phy.cam.ac.uk/teaching/exam_questions.php, and you will find a brief description of how examiners work at http://www.phy.cam.ac.uk/teaching/exam_workings.php. Internal examiners are appointed each year for each Tripos examination; two external examiners are also appointed for Parts II and III. The Reporter publishes the names of the examiners. For each subject listed below there is a Senior Examiner drawn from the staff of the Department, and they take the responsibility for the setting and marking of the examination papers, assisted by the other examiners. For the academic year 2013-14 the Senior Examiners are: Part IA Physics: Dr G A C Jones Part IB Physics A: Prof. J J Baumberg Part IB Physics B: Dr B M Gripaios Part II Physics: Dr R Padman Part II Half Subject Physics: Dr R Padman Part III Physics: Prof. D R Ward MASt: Prof. D R Ward You should note that, by tradition - in order to ensure that the examination process is beyond reproach - direct contact with the examiners is not encouraged. If you have a problem that you believe should be brought before a particular body of examiners, the proper channel is through your Tutor or Director of Studies. Selective Preparation for Examinations There has been some discussion with past students about the advisability of ‘ditching a course’ in preparation for the examinations. The Department gave the following advice:

130 Guide for Students (1) Departmental policy is that the examinations should test the whole course taken by students. The examinations are designed to test the wide range of skills and knowledge that has been acquired. (2) In any section of an examination paper, there is likely to be a range of questions which you will find to have differing degrees of difficulty and also testing different aspects of each course. (3) It is very dangerous indeed to ‘ditch courses’. It results in a very limited range of questions which can be answered - how do you know they are not all going to be very demanding? It requires enormous effort to be sure that you can answer well any question which can be set on any given course. It is much safer, and educa- tionally much sounder, to prepare for all the courses for which you are entered in the Tripos examinations. You are much more likely to find two questions out of four in which you can perform well. Examples Classes From the third year onwards Examples Classes are provided as an important aid to your learning. They explore in greater depth some particular issues related to parts of the lecture course, and with a number of demonstrators on hand they should be used to strengthen your grasp of the course material. Examples Sheets Examples sheets are provided to accompany every lecture course, and are usually distributed outside the lecture theatre. It is the policy of the Department to provide examples which cover a wide range of difficulty, so don’t expect to be able to do all of them without some assistance from your supervisor. You should try to produce satisfactory solutions to all of the designated ‘core’ examples for your subsequent use in revision, after discussion of the material in a supervision. Many of the questions are taken from past Tripos papers, so they provide good practice in handling material in the lecture courses, chosen to reflect the present content of the course. Faculty of Physics and Chemistry The Department of Physics is part of the Faculty of Physics and Chemistry. Feedback The Department makes a great effort to provide excellent courses and facilities, and obviously wishes to ensure that the results are as good as possible from the student’s perspective. We rely on you to help us iron out any problems. Your input to the constant refinement of our teaching provision is therefore a welcome and essential ingredient, and is most helpfully directed through your representative on the Staff-Student Consulta- tive Committee (see below). Feedback is now obtained using the SWIFT survey tool on Caret. Please fill these in with constructive comments – these responses are important input to the Consultative Committee, and the information is then passed on to the lecturers, Heads of Class and supervisors. There are also e-mail addresses for comments on each year of the Tripos (see the top of the relevant sections in this Handbook). Fire Alarms All buildings are equipped with fire alarms, and you should take note of the instructions, which are posted around the buildings, for the procedure to follow in case of fire. There is a fire drill at some time each year. If you hear a fire alarm leave the building quickly and quietly by the nearest fire exit. Do not stop to collect your possessions. Do not use lifts. Fire doors in corridors close automatically when the alarm system is activated; they must never be obstructed. The system is tested between 7.30am and 8.30am each Monday. If you discover a fire, raise the alarm by breaking the glass at the nearest Fire Alarm Point, and evacuate the building by the nearest safe route. If it is possible to do so without taking personal risks call the Fire Brigade (telephone 1999 from a University network telephone). Formulae A booklet of standard mathematical formulae, identical to the one that is made available in certain examinations, is available for purchase from Cavendish Stores and Classes Technicians or for downloading from the web at http://www.phy.cam.ac.uk/teaching/students.php. You are urged to use and become familiar with the contents of this booklet, because it has become clear in recent Tripos examinations that many students are not aware of the time it can save them in an examination.

Guide for Students 131 Handbook The Physics Course Handbook is updated each year, and distributed to students of all years. It aims to be the definitive source of information about the courses, but students may be informed of corrections, and up- dates, during the year, e.g. in course handouts, or by notices on notice boards, or by e-mail. It is also available on the web at http://www.phy.cam.ac.uk/teaching/students.php. Please send any comments, on errors or omissions, by e-mail to [email protected]. Harassment The University is committed to creating and maintaining an environment for work and learning which is free from all forms of discrimination. The central authorities of the University regard racial, sexual and disability harassment and bullying as wholly unacceptable behaviour. The information about harassment is available at www.admin.cam.ac.uk/offices/personnel/policy/dignity/. Any student who feels they are being harassed or bullied racially, sexually or because of a disability is encouraged to seek advice. The Department of Physics has appointed two advisors who are available to students for guidance and support: Dr Bill Allison, Room 413B & Tel: 37416, E-mail: mailto:[email protected] Dr Julia Riley, Room 916 & Tel: 37308, E-mail: [email protected] Advice may also be obtained from College Tutors. Contact with the advisors will be treated as confidential. No information about a complaint will be released or taken any further without the student’s consent. Institute of Physics The Institute of Physics is a national body that exists to promote physics. The Student Liaison Officer for the Institute of Physics is Esther Bennett ([email protected]). Prof. Mike Payne ([email protected]) is the Cambridge Representative, from whom application forms can also be obtained. Following graduation you may obtain (according to experience) various grades of professional membership, Chartered Physicist status, and several other benefits which may have some bearing on obtaining a job. Laboratory Closure The Cavendish Laboratory opens at 8:00 and closes at 18:00 Monday to Friday. Over Christmas and New Year the Laboratory is completely closed. Late Submission of Work In accordance with the University’s regulations, work submitted after the advertised deadline will not count towards your final examination mark, unless an extension of time is granted on the grounds that there are mitigating circumstances. For any item of work amounting to more than 10% of the total for the year (for example a Part III Project), any application for such an extension should be made by your college Tutor to the University’s Applications Committee. For items of work amounting to less than 10% of the total year’s mark, any application for an extension should be made by your college Tutor or Director of Studies to the Director of Undergraduate Teaching, c/o Teaching Office, Cavendish Laboratory, ([email protected]). In either case, you should submit the work as soon as possible after the deadline. Lecture handouts Handouts, containing material to supplement lectures, are usually distributed at the time of the relevant lecture outside the lecture theatre. The amount of material prepared is at the discretion of the lecturer. Diverse opinions have been (vociferously) expressed by students each year about handouts - some want very little material, others wish to have copies of lecture overheads, others want a substitute for a book. When lecture overheads are supplied there are often criticisms that the lecturer is reading from the handout! It is impossi- ble for the Department to provide courses and handouts which satisfy every different preference. Lecture handouts should be regarded as assistance beyond the lecture material, optionally provided by the lecturer, but they cannot substitute for your own reading through the wide range of textbooks available throughout the University, and you cannot reasonably expect them to. Lecture handouts are available on the web at http://www-teach.phy.cam.ac.uk/teaching/handouts.php.

132 Guide for Students Lectures Details of lectures will be found in the Lecture List published at the start of each academic year on the web at http://www.phy.cam.ac.uk/teaching/lectures.php. Part IA lectures are usually held in the Bristol-Myers Squibb Lecture Theatre, The Chemical Laboratory. Part IB Physics A and Physics B lectures are usually held in the Cockcroft Lecture Theatre on the New Muse- ums Site. Part II and Part III lectures are usually held in the lecture theatres at the Cavendish Laboratory or in the Sackler Lecture Theatre at the Institute of Astronomy. Libraries Library provision in Cambridge is outstanding. Your College will probably provide a core of physics books to supplement those you buy. Usually the College Librarian will welcome suggestions for additional purchases if you find omissions of important books from the College Library. The Department provides the Rayleigh Library, located in the Bragg building, and a special section has been set aside for use by Part II and Part III students (see Part II and Part III Library, below). The University Library has an extensive physics collection. Physics journals are held in the Rayleigh Library and in the Moore Library in Wilberforce Road (see below). Online access to many physics journals is available within the cam domain. MASt This is a taught postgraduate course, which consists of the same content as Part III Physics. The course is designed for students who hold a 3-year undergraduate degree who wish to pursue a research degree. The entry requirement for the MASt is a qualification comparable to an upper second class or better UK Bache- lor’s degree in Physics. Managed Cluster Service (MCS – formally PWF) The MCS is a network of PCs supported by the Computing Service and located close to the Practical classes. It is used to assist with data analysis, document preparation and specific computing exercises. You will need to register as a user. See also Computing (above). Printing facilities are available. Moore Library The University’s main collection of physical sciences, technology and mathematics journals is kept in the Moore Library in the Centre for Mathematical Sciences in Wilberforce Road (close to the Cavendish, just turn left at the end of the footpath leading from the Cavendish into town, instead of continuing down Adams Road; the large building on the right near the far end of the road is the CMS). To use the collection you need to have a University Card. It is unlikely to be useful to you until the Third and Fourth years. Natural Sciences Tripos The Natural Sciences Tripos (NST) is the official title of the degree examinations covering the Natural Sci- ences, including Physics. The participating Departments of the University work together to provide a wide choice of subjects which can be combined in a great variety of ways to cater for the interests of each student. Many students seem unclear about how the Part II and Part III examinations are Classed. The following is an extract from notes prepared in order to clarify the Department’s position on this: Part III of the Tripos is classed in the usual way - 1st, 2.1, 2.2, 3rd. Parts II and III of the Tripos are independent and marks are not carried forward from one to the other. Degrees as such are not classed. Students graduate from the University as a B.A. ‘with Honours’ and, if they are classed in Part III, as an M.Sci. The classes are attached to a particular Tripos. Thus if, for example, a student obtains a First in Part II, they will be entitled to say that they obtained ‘First Class Honours in Part II of the NST’ whatever their results in Part III. If they also obtain a good result in Part III then they can add that to their curriculum vitae. If future employers, postgraduate grant funding agencies, etc. require more detailed information than just the degree certificate, they will normally receive from a College or the University

Guide for Students 133 the full profile of the student’s achievements during their years here, not just their result in the final year. This should enable them to give proper weight to the Part II results. It is worth noting that many of the key decisions about job offers and places in research groups will be made before the Part III results are known, so the Part II classes are likely to be an important factor in those choices. The Research Councils normally require a specific standard to be met if students are to be eligible for postgraduate support. At present a student is eligible for a Research Council grant if at least an Upper Second has been attained in either Part II or Part III. It is unlikely that a poor result in Part III would lead to an offer of a place from any university, even if the formal requirement had been attained at Part II. See also Classing Criteria, above. Part II and Part III Library An area is set aside in the Rayleigh Library for use by Part II and Part III students, and there is an extensive collection of textbooks on all aspects of physics. These, and books from the main section of the Library, may be borrowed overnight after completing the borrowing procedure at the desk next to the main door to the Li- brary. A quiet area for study is also available in the Part II/III study area accessible from the link bridge between the Bragg and Rutherford buildings. Past Tripos papers Recent papers are also available on the web at www-teach.phy.cam.ac.uk/teaching/examPapers.php. Re- member that the course content changes, so past papers may contain questions on material with which you are not now expected to be familiar! Personal Computers Many Colleges provide PCs, and you may also use those provided in the Cavendish by the Managed Cluster Service (MCS formally PWF). See Computing (above). Philosophical Society The Philosophical Society is a long-established society in the University which, among its various functions, puts on evening lectures in the Bristol-Myers Squibb Lecture Theatre, Department of Chemistry. Some of these are by eminent physicists and all are intended for a broad audience - you are therefore most welcome to attend. More details are available at http://www.cam.ac.uk/societies/cps/. Physics Course Handbook See Handbook (above). Photocopying Photocopying may be carried out in the copy room of the Rayleigh Library, at a cost of 4p per A4 copy. Pho- tocopying can only be carried out with the purchase of a card, the lowest denomination being £1, with other amounts of £2, £5, £10, £25. Photocopy cards may be purchased in the Library. Physics Society (CUPS) The Physics Society organises a range of functions, including evening lectures. Joining is easy at the first evening lecture or at the Societies’ Fair. More details are available at www.srcf.ucam.org/physics/wiki/index.php?title=Cambridge_University_Physics_Society. Plagiarism See Cheating (above). Practical Classes The Practical Classes are an important and examinable part of your course, and are conducted in the Caven- dish Laboratory. Registration procedures are outlined in the relevant section of this Handbook. Rayleigh Library The Rayleigh Library is primarily a resource for research, but it includes a great many useful reference works as well as original research journals. Here you can also find New Scientist, Scientific American, Physics

134 Guide for Students World (for those who don’t have their own copy!) and Physics Today. All of these are excellent sources of information about the fast-advancing frontiers of physics. Next to the section with these and other current journals is the Part II & III Library. There is limited space for private working. Raven Raven is the University of Cambridge web authentication server. You will need your Raven password to log in to the Teaching Information System (q.v.), and to access "cam-only" material (such as past examination papers) on the teaching website from outside the cam.ac.uk domain. If you use the Hermes mail-store, then you can get your Raven password at https://jackdaw.cam.ac.uk/get-raven-password. If you don't use Her- mes, then you can request a Raven password from http://ww.cam.ac.uk/cs/request/raven.html. If you have a Raven password and your login is rejected by the teaching system, please let the Teaching Office know your CRSID so that we can enable your account. If you have lost your Raven password, or it doesn't work, then see http://www.cam.ac.uk/cs/docs/faq/n3.html. Recording of Lectures Audio or video recording of lectures is not generally allowed. If there is a specific reason for needing to record a lecture then a request should be made to the Teaching Office, who will consult the relevant lecturer. The Department may require that the recording is made by the lecture theatre technician. Refreshments See Common Room. Registration The Department runs an extensive set of teaching databases, and uses these, for example, to contact all students in any particular category. In order for us to reach you, we first need to know that you are here. You should receive, from the Department and/or your DoS, an invitation to register shortly before the start of the academic year. This does NOT enter you for examinations, or have any official function outside the Physics Department, but it does get you into the system so that we know you are here, and what you are doing. We are then able to allocate departmental supervisions where appropriate, and to give you access to all relevant information. Reporter The University Reporter is the official publication of the University in which announcements are made. From this year the paper version of the Reporter will no longer be produced. All notices including the lecture list and official notices concerning examination procedures see http://www.admin.cam.ac.uk/reporter/ Research The Cavendish is a large and thriving research laboratory, with a wide range of present-day interests in physics, and a fascinating and illustrious history. More information about the research can be found distributed around the laboratory in the form of poster displays, but an increasing amount of information will be found via our Home Page on the World Wide Web: http://www.phy.cam.ac.uk Research is organised into the following groups:

Abbreviation Name of Research Group Contact Phone AMOP Atomic, Mesoscopic & Optical Physics 66298 AP Astrophysics 37294 BSS Biological and Soft Systems 37423/37007 HEP High Energy Physics 37227 IG Inference 37254 ME Microelectronics 37556 OE Optoelectronics 37313 NP NanoPhotonics 60945

Guide for Students 135 QM Quantum Matter 37351 SMF Surfaces, Microstructure & Fracture 37336 SP Semiconductor Physics 37482 TCM Theory of Condensed Matter 37254 TFMM Thin Films, Magnetism & Materials 37336 Safety Safe conduct is legally the individual responsibility of everyone in the workplace, whether they be student or staff member. Additionally the Department has specific legal obligations regarding health and safety, which are monitored by the Department Safety and Environment Committee. You will be given information about health and safety in the Practical Classes in particular; please take in this information, and accord it the importance it deserves. Particular rules apply to Part III Project work; they are detailed in the section describing the arrangements for projects. The Departmental Safety Officer is Dr. Jane Blunt (Room 220, Ext. 37397, [email protected]). Scientific Periodicals Library The University’s main collection of scientific journals has been split into two. Journals related to the physical sciences, technology and mathematics are kept in the new Moore Library in the Centre for Mathematical Sci- ences in Wilberforce Road (close to the Cavendish, just turn left at the end of the footpath leading from the Cavendish into town, instead of continuing down Adams Road; the large building on the right near the far end of the road is the CMS). The other journals are kept in the SPL in Bene’t Street, which was originally the Philosophical Society’s Library and still houses the offices of the Society. To use the collection you need to have a University Library card. It is unlikely to be useful to you until the third and fourth years. Smoking The entire Department of Physics has been designated a NO SMOKING AREA. Staff-Student Consultative Committee The SSCC is the official channel for the communication of students’ concerns to the Department. There are one or two student representatives for each of the courses provided by the Department. Elections to the SSCC take place early in the Michaelmas term during lectures. The Consultative Committee is chaired by Dr Julia Riley, and the other members are the Head of Department, the Director of Undergraduate teaching and the Secretary of the Teaching Committee. The Committee meets at the end of each term, just after lectures finish, and a major part of its business is to discuss in detail the feedback on each course, particularly as reflected by questionnaires. The Committee also provides feedback to the Teaching Committee on general teaching issues. The Committee’s minutes are considered in detail by the Teaching Committee and by the Head of Depart- ment, and are made available on the web for access within Cambridge (see www.phy.cam.ac.uk/teaching/committees.php, where the current membership may also be found). Supervisions Supervisions are organised through your college for Parts IA and IB, and by the Department for Part II. Su- pervision in larger groups is organised by the Department for Part III. You are normally expected to attend every supervision which you have arranged, as a courtesy to your supervisor as well as in order to benefit your own studies. You should expect to be asked to hand in work for each supervision, in sufficient time for your supervisor to look through the work and identify any potential problems. If for some reason you have problems, please contact your Director of Studies in the first instance, even for supervisions arranged by the Department. Synopses Moderately detailed synopses are published for every course offered by the Department; the synopses have been arrived at after long deliberation, consultation, and debate within the Department. The relationship between courses is handled by the Teaching Committee, and every effort is made to refine the sequence in

136 Guide for Students which material is presented. Some problems remain; these should just be the ones for which no clear-cut solution was available, but in case there are difficulties for you which have not been identified in advance, the Staff-Student Consultative Committee always welcomes direct feedback via your representative. Teaching Committee The Teaching Committee concerns itself with all aspects of teaching in the Department of Physics. It oversees the structure of lecture courses and practicals, and weighs up information about the success of the courses regularly during the academic year. The best route for communicating information to the committee is through your representative on the Staff-Student Consultative Committee, which itself reports to the Teach- ing Committee. The Chair of the Committee is Dr John Richer (Director of Undergraduate teaching) and the Secretary Dr Dave Green. Teaching Information System The TiS is a web interface to the various teaching databases maintained by the Department. Part IA students can view their practical marks on the web; Part II and III students can select Research Reviews and Projects here, and can view their further work marks in the same way if they have been released. All supervisions arranged by the department are listed, and you can use the system as an easy way to email your supervisors and supervision partners (for Parts II and III). All handouts, for all years, are now available via the TiS, http://www-teach.phy.cam.ac.uk Note that you must first be registered (see "Registration") for the current year in order to gain access to these facilities, and that many of them require you first to log in, using your Raven password (see under "Raven"). Teaching Office The Physics Department has a Teaching Office which is situated in the Bragg building, Room 212B, tel. 65798. The Teaching Office is run by Helen Marshall and is open for general enquiries and submission of written reports at regular times during full term. Enquiries can also be made to its e-mail address: teaching- [email protected]. Telephones The internal telephone network of the university provides ‘free’ calls between extensions, most of which have a five-digit number. To reach an extension from another exchange line outside the network, the number is prefixed with a 3. (Some recent lines have 5-digit number beginning with a 6, for which the prefix when dialling from outside is a 7). For details, see the internal telephone directory. Transferable Skills We have identified a set of transferable skills that physics undergraduates can expect to acquire in Cam- bridge. As well as being needed for academic performance, these skills are sought after by employers, and students are encouraged to develop them. The details can be found on the web at http://www.phy.cam.ac.uk/teaching/students.php University Library The University Library is an amazing resource for the University (and in many disciplines, for the interna- tional academic community). You may be surprised at how useful it can be for you. However, since it is so large it can be a little complicated. Your University Card is required to gain access to the University Library. You cannot take bags etc. into the library for security reasons, but you can leave them in the metal lockers to be found down a few steps on the right hand side of the entrance hallway. The keys are released by the inser- tion of a £1 coin, which is returned to you when you open the locker. Most of the relevant physics books are to be found on the shelves in ‘South Front, Floor 4’ - easily located on the maps displayed throughout the building. You need to know that in order to maximise storage, books are shelved in catalogue sequence, but split into different size categories. This means that you might find four

Guide for Students 137 different sets of books on, say, atomic physics - the size is indicated by a letter a,b,c in the catalogue number. They are easy to find once you know this! Periodicals (‘serials’) have numbers prefixed with P. An increasing proportion of the 7,500,000 items in the inventory of the library are appearing on the computer catalogue, which can be accessed from any computer terminal which can connect to the network. The catalogue will tell you where the book should be found (eg SF4 i.e. South Front Floor 4) and whether or not it is out on loan (and if so, when it is due back). The same catalogue system allows you to check your College library catalogue (for most of the colleges) and that of the Rayleigh Library. The UL catalogue is available at http://www.lib.cam.ac.uk/. World-Wide Web The Cavendish Laboratory’s home page http://www.phy.cam.ac.uk has notices about events in the Caven- dish, lists of staff and details of the activities of the various research groups, as well as teaching material and information. This Physics Course Handbook and teaching material for various courses can be found at http://www.phy.cam.ac.uk/teaching/. The Teaching web pages also provide links to the Teaching Informa- tion system (q.v.), and to certain material that is not generally available to addresses outside the cam.ac.uk domain.

138 Guide for Students