Dynamical Phase Transitions in Quantum Mechanics Abstract

Total Page：16

File Type：pdf, Size：1020Kb

Dynamical Phase Transitions in Quantum Mechanics Abstract

Dynamical phase transitions in quantum mechanics Ingrid Rotter Max-Planck-Institut fürPhysik komplexer Systeme, D-01187 Dresden, Germany Abstract 1936 Niels Bohr: In the atom and in the nucleus we have indeed to do with two extreme cases of mechanical many-body problems for which a procedure of approximation resting on a combination of one-body problems, so effective in the former case, loses any validity in the latter where we, from the very beginning, have to do with essential collective aspects of the interplay between the constituent particles. 1963: Maria Goeppert-Mayer and J. Hans D. Jensen received the Nobel Prize in Physics for their discoveries concerning nuclear shell structure. State of the art 2011: { The nucleus is an open quantum system described by a non-Hermitian Hamilton operator with complex eigenvalues. The eigenvalues may cross in the complex plane ('exceptional points'), the phases of the eigenfunctions are not rigid in approaching the crossing points and the widths bifurcate. By this, a dynamical phase transition occurs in the many-level system. { The dynamical phase transition starts at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. { The statement of Niels Bohr for compound nucleus states at high level density is not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. { Dynamical phase transitions are observed experimentally in different systems, including PT - symmetric ones, by varying one or more parameters. References 1. Topical review J. Phys. A 42, 153001 (2009) 2. J. Opt. 12, 065701 (2010) 3. J. Mod. Phys. 1, 303 (2010) 1.

Copy Link

Recommended publications

Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman
Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman Louis de Broglie Norman Ramsey Willis Lamb Otto Stern Werner Heisenberg Walther Gerlach Ernest Rutherford Satyendranath Bose Max Born Erwin Schrödinger Eugene Wigner Arnold Sommerfeld Julian Schwinger David Bohm Enrico Fermi Albert Einstein Where discovery meets practice Center for Integrated Quantum Science and Technology IQ ST in Baden-Württemberg . Introduction “But I do not wish to be forced into abandoning strict These two quotes by Albert Einstein not only express his well more securely, develop new types of computer or construct highly causality without having defended it quite differently known aversion to quantum theory, they also come from two quite accurate measuring equipment. than I have so far. The idea that an electron exposed to a different periods of his life. The first is from a letter dated 19 April Thus quantum theory extends beyond the field of physics into other 1924 to Max Born regarding the latter’s statistical interpretation of areas, e.g. mathematics, engineering, chemistry, and even biology. beam freely chooses the moment and direction in which quantum mechanics. The second is from Einstein’s last lecture as Let us look at a few examples which illustrate this. The field of crypt it wants to move is unbearable to me. If that is the case, part of a series of classes by the American physicist John Archibald ography uses number theory, which constitutes a subdiscipline of then I would rather be a cobbler or a casino employee Wheeler in 1954 at Princeton. pure mathematics. Producing a quantum computer with new types than a physicist.” The realization that, in the quantum world, objects only exist when of gates on the basis of the superposition principle from quantum they are measured – and this is what is behind the moon/mouse mechanics requires the involvement of engineering.
[Show full text]
I. I. Rabi Papers [Finding Aid]. Library of Congress. [PDF Rendered Tue Apr
I. I. Rabi Papers A Finding Aid to the Collection in the Library of Congress Manuscript Division, Library of Congress Washington, D.C. 1992 Revised 2010 March Contact information: http://hdl.loc.gov/loc.mss/mss.contact Additional search options available at: http://hdl.loc.gov/loc.mss/eadmss.ms998009 LC Online Catalog record: http://lccn.loc.gov/mm89076467 Prepared by Joseph Sullivan with the assistance of Kathleen A. Kelly and John R. Monagle Collection Summary Title: I. I. Rabi Papers Span Dates: 1899-1989 Bulk Dates: (bulk 1945-1968) ID No.: MSS76467 Creator: Rabi, I. I. (Isador Isaac), 1898- Extent: 41,500 items ; 105 cartons plus 1 oversize plus 4 classified ; 42 linear feet Language: Collection material in English Location: Manuscript Division, Library of Congress, Washington, D.C. Summary: Physicist and educator. The collection documents Rabi's research in physics, particularly in the fields of radar and nuclear energy, leading to the development of lasers, atomic clocks, and magnetic resonance imaging (MRI) and to his 1944 Nobel Prize in physics; his work as a consultant to the atomic bomb project at Los Alamos Scientific Laboratory and as an advisor on science policy to the United States government, the United Nations, and the North Atlantic Treaty Organization during and after World War II; and his studies, research, and professorships in physics chiefly at Columbia University and also at Massachusetts Institute of Technology. Selected Search Terms The following terms have been used to index the description of this collection in the Library's online catalog. They are grouped by name of person or organization, by subject or location, and by occupation and listed alphabetically therein.
[Show full text]
The Early History of the Niels Bohr Institute
CHAPTER 4.1 Birthplace of a new physics - the early history of the Niels Bohr Institute Peter Robertson* Abstract SCI.DAN.M. The foundation in 1921 of the Niels Bohr Institute in Copenhagen was to prove an important event in the I birth of modern physics. From its modest beginnings as • ONE a small three-storey building and a handful of physicists, HUNDRED the Institute underwent a rapid expansion over the fol lowing years. Under Bohr’s leadership, the Institute provided the principal centre for the emergence of quan YEARS tum mechanics and a new understanding of Nature at OF the atomic level. Over sixty physicists from 17 countries THE came to collaborate with the Danish physicists at the In BOHR stitute during its first decade. The Bohr Institute was the ATOM: first truly international centre in physics and, indeed, one of the first in any area of science. The Institute pro PROCEEDINGS vided a striking demonstration of the value of interna tional cooperation in science and it inspired the later development of similar centres elsewhere in Europe and FROM the United States. In this article I will discuss the origins and early development of the Institute and examine the A CONFERENCE reasons why it became such an important centre in the development of modern physics. Keywords: Niels Bohr Institute; development of quan tum mechanics; international cooperation in science. * School of Physics, University of Melbourne, Melbourne, Vic. 3010, Australia. Email: [email protected]. 481 PETER ROBERTSON SCI.DAN.M. I 1. Planning and construction of the Institute In 1916 Niels Bohr returned home to Copenhagen over four years since his first visit to Cambridge, England, and two years after a second visit to Manchester, working in the group led by Ernest Ru therford.
[Show full text]
Enrico Fermi: Genius
ANNIVERSARY Enrico Fermi: genius This year marks the centenary of the birth of Enrico Fermi, one of the giants of 20th- • century science, and one of the last physicists to be both an accomplished experimentalist and an influential theorist. Here, Gianni Battimelli of the University of Rome "La Sapienza" traces the life of a genius. Enrico Fermi was born on 29 September 1901 in Rome to a family with no scientific traditions. His passion for natural sciences, and in particular for physics, was stimulated and guided in his school years by an engineer and family friend, Adolph Amidei, who recognized Fermi's exceptional intellectual abilities and suggested admission to Pisa's Scuola Normale Superiore. After finishing high-school studies in Rome, in 1918 Fermi progressed to the prestigious Pisa Institute, after producing for the admission exam an essay on the characteristics of the propagation of sound, the authenticity of which the commissioners initially refused to believe. Studies at Pisa did not pose any particular difficulties for the young Fermi, despite his having to be largely self-taught using mate rial in foreign languages because nothing existed at the time in Fermi's group discovered the Italian on the new physics emerging around relativity and quantum radioactivity induced by theory. In those years in Italy, these new theories were absent from university teaching, and only mathematicians likeTullio Levi-Civita neutrons, instead of the had the knowledge and insight to see their implications. alpha particles used in the Working alone, between 1919 and 1922, Fermi built up a solid competence in relativity, statistical mechanics and the applications Paris experiments.
[Show full text]
Release of Documents Relating to 1941 Bohr-Heisenberg Meeting
Release of documents relating to 1941 Bohr-Heisenberg meeting DOCUMENTS RELEASED 6 FEBRUARY 2002 The family of Niels Bohr has decided to release all documents deposited at the Niels Bohr Archive, either written or dictated by Niels Bohr, pertaining specifically to the meeting between Bohr and Heisenberg in September 1941. There are in all eleven documents. The decision has been made in order to avoid possible misunderstandings regarding the contents of the documents. The documents supplement and confirm previously published statements of Bohr's recollections of the meeting, especially those of his son, Aage Bohr. The documents have now been organised, transcribed and translated into English at the Niels Bohr Archive. Because of the overwhelming interest in the material, it has been decided that the material should be published in full instead of being made available to scholars upon individual application, as is normal practice at the Niels Bohr Archive. This has been done by placing facsimiles, transcriptions and translations on this website here. An illustrated edition of the transcriptions and translations is published in the journal Naturens Verden, Vol. 84, No. 8 - 9. Reprints can be obtained from the Niels Bohr Archive for USD8/EUR8/DKK50 (prepaid). Release of documents relating to 1941 Bohr-Heisenberg meeting. Document 1. Draft of letter from Bohr to Heisenberg, never sent. In the handwriting of Niels Bohr's assistant, Aage Petersen. Undated, but written after the first publication, in 1957, of the Danish translation of Robert Jungk, Heller als Tausend Sonnen, the first edition of Jungk's book to contain Heisenberg's letter.
[Show full text]
Absolute Zero, Absolute Temperature. Absolute Zero Is the Lowest
Contents Radioactivity: The First Puzzles................................................ 1 The “Uranic Rays” of Henri Becquerel .......................................... 1 The Discovery ............................................................... 2 Is It Really Phosphorescence? .............................................. 4 What Is the Nature of the Radiation?....................................... 5 A Limited Impact on Scientists and the Public ............................ 6 Why 1896? .................................................................. 7 Was Radioactivity Discovered by Chance? ................................ 7 Polonium and Radium............................................................. 9 Marya Skłodowska .......................................................... 9 Pierre Curie .................................................................. 10 Polonium and Radium: Pierre and Marie Curie Invent Radiochemistry.. 11 Enigmas...................................................................... 14 Emanation from Thorium ......................................................... 17 Ernest Rutherford ........................................................... 17 Rutherford Studies Radioactivity: ˛-and ˇ-Rays.......................... 18 ˇ-Rays Are Electrons ....................................................... 19 Rutherford in Montreal: The Radiation of Thorium, the Exponential Decrease........................................... 19 “Induced” and “Excited” Radioactivity .................................... 20 Elster
[Show full text]
Guide to the James Franck Papers 1882-1966
University of Chicago Library Guide to the James Franck Papers 1882-1966 © 2006 University of Chicago Library Table of Contents Acknowledgments 3 Descriptive Summary 3 Information on Use 3 Access 3 Citation 3 Biographical Note 4 Scope Note 15 Related Resources 21 Subject Headings 21 INVENTORY 22 Series I: Correspondence 22 Series II: Manuscripts 51 Subseries 1: Physics - work in Germany and Denmark, 1905-1934 51 Subseries 2: Physics - work in United States, 1935-1958 53 Subseries 3: Biophysics - work on Photosynthesis at Johns Hopkins, 1935-193855 Subseries 4: Biophysics - work on Photosynthesis at the University of Chicago,55 1938-48 Subseries 5: Biophysics - work on Photosynthesis after 1948 55 Subseries 6: General Articles and Talks on Science 71 Subseries 7: Papers by other scientists 72 Subseries 8: Notes, memoranda and fragments 76 Subseries 9: Atomic Scientists' Movement, 1944-1953 76 Subseries 10: Franck Memorial Symposium, May 12-13, 1966 79 Series III: Tape Recordings and Photographs 80 Subseries 1: Tape recordings 80 Subseries 2: Hertha Sponer's photograph album, Göttingen, 1920-1933 80 Series IV: Personal Documents and Memorabilia 90 Subseries 1: Documents 90 Subseries 2: Clippings 93 Subseries 3: Biographies and Obituaries 94 Subseries 4: Memorabilia; Scrolls, Certificates, Medals, Mementos 96 Series V: Robert Platzman's Editorial Papers for the "Selected Works of James98 Franck" Series VI: Addenda 103 Subseries 1: Correspondence between James Franck and his nephew and Dr. Heinz104 Kallman Subseries 2: Oversize 105 Descriptive Summary Identifier ICU.SPCL.FRANCK Title Franck, James. Papers Date 1882-1966 Size 20.5 linear feet (29 boxes) Repository Special Collections Research Center University of Chicago Library 1100 East 57th Street Chicago, Illinois 60637 U.S.A.
[Show full text]
Nuclear Proliferation International History Project
Nuclear Proliferation International History Project Political Authority or Atomic Celebrity? The Influence of J. Robert Oppenheimer on American Nuclear Policy after the Second World War By Marco Borghi NPIHP Working Paper #14 August 2019 THE NUCLEAR PROLIFERATION INTERNATIONAL HISTORY PROJECT WORKING PAPER SERIES Christian F. Ostermann and Leopoldo Nuti, Series Editors This paper is one of a series of Working Papers published by the Nuclear Proliferation International History Project. The Nuclear Proliferation International History Project (NPIHP) is a global network of individuals and institutions engaged in the study of international nuclear history through archival documents, oral history interviews and other empirical sources. Recognizing that today’s toughest nuclear challenges have deep roots in the past, NPIHP seeks to transcend the East vs. West paradigm to work towards an integrated international history of nuclear weapon proliferation. The continued proliferation of nuclear weapons is one of the most pressing security issues of our time, yet the empirically-based study of international nuclear history remains in its infancy. NPIHP’s programs to address this central issue include: • the annual Nuclear Boot Camp for M.A. and Ph.D. candidates to foster a new generation of experts on the international history of nuclear weapons; • the NPIHP Fellowship Program for advanced Ph.D. students and post-doctoral researchers hosted by NPIHP partner institutions around the world; • a coordinated, global research effort which combines archival mining and oral history interviews conducted by NPIHP partners; • a massive translation and digitization project aimed at making documentary evidence on international nuclear history broadly accessible online; • a series of conferences, workshops and seminars hosted by NPIHP partners around the world.
[Show full text]
History of the Development of Atomic Theory READINGS.Pdf
Collaborative Learning Activity – How is it we have come to understand the inner workings of the atom? You will be split between several Groups, dependent on class size. In each group you will be responsible for a specific volume of the material. As “experts” you must be able to teach your part of the information regarding the historical development of the present-day model of the atom to others in each group. You will create a timeline of historical figures and brief sketches of each model of the atom as it evolved into what science now understands regarding the atom. The biographical information presented is important, but your main focus should be on the scientific contributions and experimentation that have guided physicists to present day understanding of the nature of the atom. Home Groups 1-6 Select Experts A - F rotate between Home Groups, Experts stay put. Activity: Step one day one. As a group, identify and illustrate the historical developments relevant to the structure of the atom as it came to be known during the period assigned to your group. Devise a plan to present to various Home Groups the following day. We will explore and highlight key developments from the ancient Greeks till now. Step two – Preparation: Finalize any of your research and Expert Graphic Organizer for presenting to Home Groups. Step three day two. Selected experts will rotate around the room and present their findings. Complete Timeline and sketches of the various models. Step four - Preparation: Complete / finalize any notes you miss. https://www.slideshare.net/mrtangextrahelp/02-a-bohr-rutherford-diagrams-and-lewis-dot-diagrams 1 Group 1 - Group 1 - Group 1 - Group 1 - Group 1 - Group 1 Do atoms exist? One of the most remarkable features of atomic theory is that even today, after hundreds of years of research, no one has yet “seen” a single atom.
[Show full text]
A Tribute to Enrico Fermi
A TriBuTE To ENriCo FErMi * henk Kubbinga * University of Groningen (The Netherlands) * DOI: 10.1051/ epn /2009803 In the history of physics, Italy has a place of its own. The hightimes of Galileo and Torricelli were followed by those of Galvani and Volta. But not much happened after 1830. Early in the 20 th century, though, the spirit of Galileo seemed to be reincarnated in Enrico Fermi (1901-1954). s a youngster, Fermi attended the public Einstein, Kronig and Goudsmit. At the time the quanti - schools of Rome, learned Latin and Greek, zation of a ‘gas’ of equal particles had his particular and had no trouble in reciting poems [1]. attention. In 1926 this research gave way to his first AAer the baccalaureat he enrolled at the major contribution to theoretical physics; it was on the Scuola Normale Superiore, at Pisa, to study mathematics ‘Quantization of the ideal monoatomic gas’. e leading and the language of science, i.e. German. e charming idea was to treat the translation of molecules between lad soon taught his teachers: as a second year’s student he the parallel walls of a container as a periodic, and there - lectured on the quantum theory and the Bohr-Som - fore quantizable, phenomenon. Instead of the container merfeld atom. Fermi’s first post-doc trip abroad was to Fermi, next, posited a radial potential field around a cen - Göttingen, the contemporary Mecca of theoretical phy - tral point – say, the origin of a Cartesian system of sics. ere he worked with Max Born and the latter’s axes –, much like the Bohr-Sommerfeld atom.
[Show full text]
James Franck 1882-1964. Biographical Memoirs of Fellows of the Royal Society 11:53-74 (With Bibliography of J
NATIONAL ACADEMY OF SCIENCES JAMES FRANCK 1 8 8 2 — 1 9 6 4 A Biographical Memoir by STUART A. RICE AND JOSHUA JORTNER Any opinions expressed in this memoir are those of the authors and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 2010 NATIONAL ACADEMY OF SCIENCES WASHINGTON, D.C. JAMES FRANCK August 26, 1882–May 21, 1964 B Y STUART A. RICE AND JOSHUA JORTNER OST SCIENTISTS EARN RECOGNITION FROM THE QUALITY of their Mcontributions to the development of our understanding of nature, some earn recognition because of the public stances they take, at personal peril, on moral issues, and some earn recognition by the positions they take on important issues at the intersection of science and politics. Only a very few earn recognition for all three reasons. James Franck was one such scientist. He made early very important contributions to the experimental basis for the quantum mechanical description of atoms and molecules, for which he was awarded the Nobel Prize in Physics in 1925, and to the understanding of the physical processes underlying photochemical processes and reactions. He was elected to membership in the National Academy of Sciences in 1944. Franck was one of the first, and one of the very few, to openly demonstrate against the racial laws introduced by the Nazi regime in Germany, and in 1933 he resigned from the University of Göttingen as a personal protest against the Nazi regime. As the principal author of a June 1945 report that attempted to convince the United States to provide a public demonstration of the first nuclear bomb before deploying it against Japan, he played a major role in the unsuccessful effort to abort an international race for supremacy in nuclear 4 BIO G RA P HICAL MEMOIRS armaments, and he played an important background role in the successful effort to achieve civilian control of nuclear power in the United States.
[Show full text]
Copenhagen, a Play by Michael Frayn
© Boldizsar Janko, March 2002 (This is a talk given before the opening show of “Copenhagen”, at The Morris Performing Art Center, South Bend, IN on March 1, 2000) March 1, 2002 I am not aware of any theatrical play in recent memory, or movie, or TV series, for that matter, that is so intensely loaded with scientific content, and nevertheless so incredibly successful as Michael Frayn’s ‘Copenhagen’. The spectacular success of the play in London, New York and Berlin came as a shock to Michael Frayn himself (yes, you guessed it, the author and various directors thought it’s wiser to test things out in smaller cities before bringing the play to Metropolitan South Bend). In March 2000, Michael Frayn was scratching his head and shifting his eyeglasses constantly as he confessed to the following in front of a huge, jam-packed auditorium [quote]: “As I sat in front of my word processor four or five years ago, struggling with this intractable massive material, struggling to understand the outline of the physics involved, struggling to understand the history of the period, struggling to find some shape of what I wanted to say, I lost all faith that the play was ever going to be produced. It seemed to me that I was writing it for my own benefit, that noone was ever going to put on this incredibly abstract remote piece, and even if anyone did, the idea that anyone would come and see it certainly never occured to me.” [end quote]. Well, as his science goes, Mr. Frayn is definitely too modest.
[Show full text]