DOCSLIB.ORG

Quantum Theory: Concepts and Methods Fundamental Theories of Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Theory: Concepts and Methods Fundamental Theories of Physics Quantum Theory: Concepts and Methods Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE University of Denver, U. S. A. Editorial Advisory Board: L. P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. GÜNTER LUDWIG, Philipps-Universität, Marburg, Germany A. PERES, Israel Institute of Technology, Israel NATHAN ROSEN, Israel Institute of Technology, Israel MENDEL SACHS, State University of New York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 72 Quantum Theory: Concepts and Methods by Asher Peres Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT,LONDON , MOSCOW eBook ISBN: 0-306-47120-5 Print ISBN 0-792-33632-1 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com To Aviva Six reviews on Quantum Theory: Concepts and Methods by Asher Peres Peres has given us a clear and fully elaborated statement of the epistemology of quantum mechanics, and a rich source of examples of how ordinary questions can be posed in the theory, and of the extraordinary answers it sometimes provides. It is highly recommended both to students learning the theory and to those who thought they already knew it. A. Sudbery, Physics World (April 1994) Asher Peres has produced an excellent graduate level text on the conceptual framework of quantum mechanics . This is a well-written and stimulating book. It concentrates on the basics, with timely and contemporary examples, is well-illustrated and has a good bibliography . I thoroughly enjoyed reading it and will use it in my own teaching and research . it is a beautiful piece of real scholarship which I recommend to anyone with an interest in the fundamentals of quantum physics. P. Knight, Contemporary Physics (May 1994) Peres’s presentations are thorough, lucid, always scrupulously honest, and often provocative . the discussion of chaos and irreversibility is a gem—not because it solves the puzzle of irreversibility, but because Peres consistently refuses to take the easy way out . This book provides a marvelous introduction to conceptual issues at the foundations of quantum theory. It is to be hoped that many physicists are able to take advantage of the opportunity. C. Caves, Foundations of Physics (Nov. 1994) I like that book and would recommend it to anyone teaching or studying quantum mechanics . Peres does an excellent job of reviewing or explaining the necessary techniques . the reader will find lots of interesting things in the book . M. Mayer, Physics Today (Dec. 1994) Setting the record straight on the conceptual meaning of quantum mechanics can be a perilous task . Peres achieves this task in a way that is refreshingly original, thought provoking, and unencumbered by the kind of doublethink that sometimes leaves onlookers more confused than enlightened . the breadth of this book is astonishing: Peres touches on just about anything one would ever want to know about the foundations of quantum mechanics . If you really want to be proficient with the theory, an honest, “no-nonsense” book like Peres’s is the perfect place to start; for in so many places it supplants many a standard quantum theory text. R. Clifton, Foundations of Physics (Jan. 1995) This book provides a good introduction to many important topics in the foundations of quantum mechanics . It would be suitable as a textbook in a graduate course or a guide to individual study . Although the boundary between physics and philosophy is blurred in this area, this book is definitely a work of physics. Its emphasis is on those topics that are the subject of active research and on which considerable progress has been made on recent years . To enhance its use as a textbook, the book has many problems embedded throughout the text . [The chapter on] information and thermodynamics contains many interesting results, not easily found elsewhere . A chapter is devoted to quantum chaos, its relation to classical chaos, and to irreversibility. These are subjects of ongoing current research, and this introduction from a single, clearly expressed point of view is very useful . The final chapter is devoted to the measuring process, about which many myths have arisen, and Peres quickly dispatches many of them . L. Ballentine, American Journal of Physics (March 1995) Table of Contents Preface xi PART I: GATHERING THE TOOLS Chapter 1: Introduction to Quantum Physics 3 l-1. The downfall of classical concepts 3 l-2. The rise of randomness 5 l-3. Polarized photons 7 l-4. Introducing the quantum language 9 l-5. What is a measurement? 14 l-6. Historical remarks 18 l-7. Bibliography 21 Chapter 2: Quantum Tests 24 2-1. What is a quantum system? 24 2-2. Repeatable tests 27 2-3. Maximal quantum tests 29 2-4. Consecutive tests 33 2-5. The principle of interference 36 2-6. Transition amplitudes 39 2-7. Appendix: Bayes’s rule of statistical inference 45 2-8. Bibliography 47 Chapter 3: Complex Vector Space 48 3-1. The superposition principle 48 3-2. Metric properties 51 3-3. Quantum expectation rule 54 3-4. Physical implementation 57 3-5. Determination of a quantum state 58 3-6. Measurements and observables 62 3-7. Further algebraic properties 67 vii viii Table of Contents 3-8.Quantum mixtures 72 3-9.Appendix: Dirac’s notation 77 3-10. Bibliography 78 Chapter 4: Continuous Variables 79 4-1.Hilbert space 79 4-2.Linear operators 84 4-3.Commutators and uncertainty relations 89 4-4.Truncated Hilbert space 95 4-5.Spectral theory 99 4-6.Classification of spectra 103 4-7.Appendix: Generalized functions 106 4-8.Bibliography 112 PART II: CRYPTODETERMINISM AND QUANTUM INSEPARABILITY Chapter 5: Composite Systems 115 5-l.Quantum correlations 115 5-2.Incomplete tests and partial traces 121 5-3.The Schmidt decomposition 123 5-4.Indistinguishable particles 126 5-5.Parastatistics 131 5-6.Fock space 137 5-7.Second quantization 142 5-8.Bibliography 147 Chapter 6: Bell’s Theorem 148 6-1.The dilemma of Einstein, Podolsky, and Rosen 148 6-2.Cryptodeterminism 155 6-3.Bell’s inequalities 160 6-4.Some fundamental issues 167 6-5.Other quantum inequalities 173 6-6.Higher spins 179 6-7.Bibliography 185 Chapter 7: Contextuality 187 7-1.Nonlocality versus contextuality187 7-2.Gleason’s theorem 190 7-3.The Kochen-Specker theorem 196 7-4.Experimental and logical aspects of contextuality 202 7-5.Appendix: Computer test for Kochen-Specker contradiction209 7-6.Bibliography 211 Table of Contents ix PART III: QUANTUM DYNAMICS AND INFORMATION Chapter 8: Spacetime Symmetries 215 8-1. What is a symmetry? 215 8-2. Wigner’s theorem 217 8-3. Continuous transformations 220 8-4. The momentum operator 225 8-5. The Euclidean group 229 8-6. Quantum dynamics 237 8-7. Heisenberg and Dirac pictures 242 8-8. Galilean invariance 245 8-9. Relativistic invariance 249 8-10. Forms of relativistic dynamics 254 8-11. Space reflection and time reversal 257 8-12. Bibliography 259 Chapter 9: Information and Thermodynamics 260 9-1. Entropy 260 9-2. Thermodynamic equilibrium 266 9-3. Ideal quantum gas 270 9-4. Some impossible processes 275 9-5. Generalized quantum tests 279 9-6. Neumark’s theorem 285 9-7. The limits of objectivity 289 9-8. Quantum cryptography and teleportation 293 9-9. Bibliography 296 Chapter 10: Semiclassical Methods 298 10-1. The correspondence principle 298 10-2.Motion and distortion of wave packets 302 10-3. Classical action 307 10-4. Quantum mechanics in phase space 312 10-5. Koopman’s theorem 317 10-6. Compact spaces 319 10-7. Coherent states 323 10-8. Bibliography 330 Chapter 11: Chaos and Irreversibility 332 11-1. Discrete maps 332 11-2. Irreversibility in classical physics 341 11-3. Quantum aspects of classical chaos 347 11-4. Quantum maps 351 11-5. Chaotic quantum motion 353 x Table of Contents 11-6. Evolution of pure states into mixtures 369 11-7. Appendix: P OST SCRIPT code for a map 370 11-8. Bibliography 371 Chapter 12: The Measuring Process 373 12-1. The ambivalent observer 373 12-2. Classical measurement theory 378 12-3. Estimation of a static parameter 385 12-4. Time-dependent signals 387 12-5. Quantum Zeno effect 392 12-6. Measurements of finite duration 400 12-7. The measurement of time 405 12-8. Time and energy complementarity 413 12-9. Incompatible observables 417 12-10. Approximate reality 423 12-11. Bibliography 428 Author Index 430 Subject Index 435 Preface There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes.
Load more

Recommended publications
  • Theoretical Physics
    IC/80/166 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS AW EFFICIENT KORRINGA-KOHN-ROSTOKER METHOD FOR "COMPLEX" LATTICES M. Yussouff and INTERNATIONAL ATOMIC ENERGY R. Zeller AGENCY UNITED NATIONS EDUCATIONAL SCIENTIFIC AND CULTURAL ORGANIZATION 19R0 MIRAMARE-TRIESTE IC/90/166 The well known rapid convergence and precision of the KKR- Green's function method (Korringa 1947, Kohn and Rostocker 1954) International Atomic Energy Agency have made it useful for the calculation of the electronic struc- and United Rations Educational Scientific and Cultural Organization ture of perfect as well as disordered solids (Ham and Segall 1961, IHTEBSATIOHAL CENTRE FOR THEORETICAL PHYSICS Ehrenrelch and Schwartz 1976). Although extensive calculations of this kind exist for cubic crystals (Moruzzi, Janak and Williams 1978), there are so far very few calculations for the equally important class of hexagonal close packed solids. This is due to the computational efforts involved in evaluating the KKR matrix AH EFFICIENT KORRIHGA-KOHH-ROSTOKER METHOD FOR "COMPLEX" LATTICES • elements ATT,{k,E) using the conventional KKR for 'complex' lattices, i.e. crystals with several atoms per unit cell- Some simplifications can be achieved (Bhokare and Yussouff 1972, 1974) for k" vectors International Centre for Theoretical Physics, Trieste, Italy, in symmetry directions but the renewed interest in simplifying the and computations (Segall and Yang 19 80) has arisen in connection with self-consistent calcualtions. Here we describe an efficient modi- R. Zeller Institut fur FeBtkorperforschung der Kernforschungsanlage, fication of the KKR method which is particularly useful for 'complex1 D-5170 Jiilieh, Federal Republic of Germany. lattices. ABSTRACT In our approach, the transformed KKR matrix elements are calcu- We present a modification of the exact KKR-band structure method lated directly using reciprocal space summation.
    [Show full text]
  • |||GET||| Can the Laws of Physics Be Unified? 1St Edition
    CAN THE LAWS OF PHYSICS BE UNIFIED? 1ST EDITION DOWNLOAD FREE Paul Langacker | 9781400885503 | | | | | Can the Laws of Physics be Unified? Answer Key. In American physicist Sheldon Glashow proposed that the weak nuclear forceelectricity and magnetism could arise Can the Laws of Physics Be Unified? 1st edition a partially unified electroweak theory. Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. In the s Mendel Sachs proposed a generally covariant field theory that did not require recourse to renormalisation or perturbation theory. Discoveries are made; models, theories, and laws are formulated; and the beauty of the physical universe is made more sublime for the insights gained. Download as PDF Printable version. Lots of equations, but not much detail explaining exactly what they mean, for that some background is needed. I find that literally inconceivable. These laws are Can the Laws of Physics Be Unified? 1st edition systematically to topics such as phase equilibria, chemical reactions, external forces, fluid-fluid surfaces and interfaces, and anisotropic crystal-fluid interfaces. Cohen and A. The physical universe is enormously complex in its detail. One of her daughters also won a Nobel Prize. Archived from the original PDF on 31 March Thank you for posting a review! And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is the end result of that process. I know of none whatsoever. Paul Langacker is senior scientist at Princeton University, visitor at the Institute for Advanced Study in Princeton, and professor emeritus of physics at the University of Pennsylvania.
    [Show full text]
  • Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations
    Article Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations Jen-Tsung Hsiang 1,*,† and Bei-Lok Hu 2,† ID 1 Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China 2 Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742-4111, USA; [email protected] * Correspondence: [email protected]; Tel.: +86-21-3124-3754 † These authors contributed equally to this work. Received: 26 April 2018; Accepted: 30 May 2018; Published: 31 May 2018 Abstract: Identifying or constructing a fine-grained microscopic theory that will emerge under specific conditions to a known macroscopic theory is always a formidable challenge. Thermodynamics is perhaps one of the most powerful theories and best understood examples of emergence in physical sciences, which can be used for understanding the characteristics and mechanisms of emergent processes, both in terms of emergent structures and the emergent laws governing the effective or collective variables. Viewing quantum mechanics as an emergent theory requires a better understanding of all this. In this work we aim at a very modest goal, not quantum mechanics as thermodynamics, not yet, but the thermodynamics of quantum systems, or quantum thermodynamics. We will show why even with this minimal demand, there are many new issues which need be addressed and new rules formulated. The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior contains elements, such as quantum coherence, correlations, entanglement and fluctuations, that are not well recognized in traditional thermodynamics, built on large systems vanishingly weakly coupled to a non-dynamical reservoir.
    [Show full text]
  • Quantum Mechanics from General Relativity : Particle Probability from Interaction Weighting
    Annales de la Fondation Louis de Broglie, Volume 24, 1999 25 Quantum Mechanics From General Relativity : Particle Probability from Interaction Weighting Mendel Sachs Department of Physics State University of New York at Bualo ABSTRACT. Discussion is given to the conceptual and mathemat- ical change from the probability calculus of quantum mechanics to a weighting formalism, when the paradigm change takes place from linear quantum mechanics to the nonlinear, holistic eld theory that accompanies general relativity, as a fundamental theory of matter. This is a change from a nondeterministic, linear theory of an open system of ‘particles’ to a deterministic, nonlinear, holistic eld the- ory of the matter of a closed system. RESUM E. On discute le changement conceptuel et mathematique qui fait passer du calcul des probabilites de la mecanique quantique a un formalisme de ponderation, quand on eectue le changement de paradigme substituantalam ecanique quantique lineairelatheorie de champ holistique non lineaire qui est associee alatheorie de la relativitegenerale, prise comme theorie fondamentale de la matiere. Ce changement mene d’une theorie non deterministe et lineaire decrivant un systeme ouvert de ‘particules’ a une theorie de champ holistique, deterministe et non lineaire, de la matiere constituant un systeme ferme. 1. Introduction. In my view, one of the three most important experimental discov- eries of 20th century physics was the wave nature of matter. [The other two were 1) blackbody radiation and 2) the bending of a beam of s- tarlight as it propagates past the vicinity of the sun]. The wave nature of matter was predicted in the pioneering theoretical studies of L.
    [Show full text]
  • The Quantum Thermodynamics Revolution
    I N F O R M A T I O N T H E O R Y The Quantum Thermodynamics Revolution By N A T A L I E W O L C H O V E R May 2, 2017 As physicists extend the 19th­century laws of thermodynamics to the quantum realm, they’re rewriting the relationships among energy, entropy and information. 48 Ricardo Bessa for Quanta Magazine In his 1824 book, Reflections on the Motive Power of Fire, the 28- year-old French engineer Sadi Carnot worked out a formula for how efficiently steam engines can convert heat — now known to be a random, diffuse kind of energy — into work, an orderly kind of energy that might push a piston or turn a wheel. To Carnot’s surprise, he discovered that a perfect engine’s efficiency depends only on the difference in temperature between the engine’s heat source (typically a fire) and its heat sink (typically the outside air). Work is a byproduct, Carnot realized, of heat naturally passing to a colder body from a warmer one. Carnot died of cholera eight years later, before he could see his efficiency formula develop over the 19th century into the theory of thermodynamics: a set of universal laws dictating the interplay among temperature, heat, work, energy and entropy — a measure of energy’s incessant spreading from more- to less-energetic bodies. The laws of thermodynamics apply not only to steam engines but also to everything else: the sun, black holes, living beings and the entire universe. The theory is so simple and general that Albert Einstein deemed it likely to “never be overthrown.” Yet since the beginning, thermodynamics has held a singularly strange status among the theories of nature.
    [Show full text]
  • Quantum Thermodynamics and Quantum Coherence Engines
    Turkish Journal of Physics Turk J Phys (2020) 44: 404 – 436 http://journals.tubitak.gov.tr/physics/ © TÜBİTAK Review Article doi:10.3906/fiz-2009-12 Quantum thermodynamics and quantum coherence engines Aslı TUNCER∗, Özgür E. MÜSTECAPLIOĞLU Department of Physics, College of Sciences, Koç University, İstanbul, Turkey Received: 17.09.2020 • Accepted/Published Online: 20.10.2020 • Final Version: 30.10.2020 Abstract: The advantages of quantum effects in several technologies, such as computation and communication, have already been well appreciated. Some devices, such as quantum computers and communication links, exhibiting superiority to their classical counterparts, have been demonstrated. The close relationship between information and energy motivates us to explore if similar quantum benefits can be found in energy technologies. Investigation of performance limits fora broader class of information-energy machines is the subject of the rapidly emerging field of quantum thermodynamics. Extension of classical thermodynamical laws to the quantum realm is far from trivial. This short review presents some of the recent efforts in this fundamental direction. It focuses on quantum heat engines and their efficiency boundswhen harnessing energy from nonthermal resources, specifically those containing quantum coherence and correlations. Key words: Quantum thermodynamics, quantum coherence, quantum information, quantum heat engines 1. Introduction Nowadays, we enjoy an unprecedented degree of control on physical systems at the quantum level. Quantum technologies promise exciting developments of machines, such as quantum computers, which can be supreme to their classical counterparts [1]. Learning from the history of industrial revolutions (IRs) associated with game- changing inventions such as steam engines, lasers, and computers, the natural question is the fundamental limits of those promised machines of quantum future.
    [Show full text]
  • Fundamental Nature of the Fine-Structure Constant Michael Sherbon
    Fundamental Nature of the Fine-Structure Constant Michael Sherbon To cite this version: Michael Sherbon. Fundamental Nature of the Fine-Structure Constant. International Journal of Physical Research , Science Publishing Corporation 2014, 2 (1), pp.1-9. 10.14419/ijpr.v2i1.1817. hal-01304522 HAL Id: hal-01304522 https://hal.archives-ouvertes.fr/hal-01304522 Submitted on 19 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Fundamental Nature of the Fine-Structure Constant Michael A. Sherbon Case Western Reserve University Alumnus E-mail: michael:sherbon@case:edu January 17, 2014 Abstract Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler’s view of nature and Pythagorean geometry. The Laplace limit of Kepler’s equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger’s research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics.
    [Show full text]
  • Quantum Theory Needs No 'Interpretation'
    Quantum Theory Needs No ‘Interpretation’ But ‘Theoretical Formal-Conceptual Unity’ (Or: Escaping Adán Cabello’s “Map of Madness” With the Help of David Deutsch’s Explanations) Christian de Ronde∗ Philosophy Institute Dr. A. Korn, Buenos Aires University - CONICET Engineering Institute - National University Arturo Jauretche, Argentina Federal University of Santa Catarina, Brazil. Center Leo Apostel fot Interdisciplinary Studies, Brussels Free University, Belgium Abstract In the year 2000, in a paper titled Quantum Theory Needs No ‘Interpretation’, Chris Fuchs and Asher Peres presented a series of instrumentalist arguments against the role played by ‘interpretations’ in QM. Since then —quite regardless of the publication of this paper— the number of interpretations has experienced a continuous growth constituting what Adán Cabello has characterized as a “map of madness”. In this work, we discuss the reasons behind this dangerous fragmentation in understanding and provide new arguments against the need of interpretations in QM which —opposite to those of Fuchs and Peres— are derived from a representational realist understanding of theories —grounded in the writings of Einstein, Heisenberg and Pauli. Furthermore, we will argue that there are reasons to believe that the creation of ‘interpretations’ for the theory of quanta has functioned as a trap designed by anti-realists in order to imprison realists in a labyrinth with no exit. Taking as a standpoint the critical analysis by David Deutsch to the anti-realist understanding of physics, we attempt to address the references and roles played by ‘theory’ and ‘observation’. In this respect, we will argue that the key to escape the anti-realist trap of interpretation is to recognize that —as Einstein told Heisenberg almost one century ago— it is only the theory which can tell you what can be observed.
    [Show full text]
  • Quantum Thermodynamics of Single Particle Systems Md
    www.nature.com/scientificreports OPEN Quantum thermodynamics of single particle systems Md. Manirul Ali, Wei‑Ming Huang & Wei‑Min Zhang* Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two‑level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system‑reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system‑reservoir coupling regime where the Born‑Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non- Markovian memory efect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by infationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The infationary dynamics may also relate to the origin of big bang and universe infation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved. In the past decade, many eforts have been devoted to understand how, starting from an isolated quantum system evolving under Hamiltonian dynamics, equilibration and efective thermodynamics emerge at long times1–5.
    [Show full text]
  • What Is Quantum Thermodynamics?
    What is Quantum Thermodynamics? Gian Paolo Beretta Universit`a di Brescia, via Branze 38, 25123 Brescia, Italy What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? For everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. How- ever, as already recognized by Schr¨odinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism of ordinary quantum theory, so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility, we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation non-equilibrium dynamics. In this long introductory paper we discuss the background and formalism of Quantum Thermo- dynamics including its nonlinear equation of motion and the main general results regarding the nonequilibrium irreversible dynamics it entails.
    [Show full text]
  • Similarity Between Quantum Mechanics and Thermodynamics: Entropy, Temperature, and Carnot Cycle
    Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle Sumiyoshi Abe1,2,3 and Shinji Okuyama1 1 Department of Physical Engineering, Mie University, Mie 514-8507, Japan 2 Institut Supérieur des Matériaux et Mécaniques Avancés, 44 F. A. Bartholdi, 72000 Le Mans, France 3 Inspire Institute Inc., Alexandria, Virginia 22303, USA Abstract Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one. PACS number(s): 03.65.-w, 05.70.-a 1 In their work [1], Bender, Brody, and Meister have developed an interesting discussion about a quantum-mechanical analogue of the Carnot engine. They have treated a two-state model of a single particle confined in a one-dimensional potential well with width L and have considered reversible cycle. Using the “internal” energy, E (L) = ψ H ψ , they define the pressure (i.e., the force, because of the single dimensionality) as f = − d E(L) / d L , where H is the system Hamiltonian and ψ is a quantum state. Then, the analogue of “isothermal” process is defined to be f L = const.
    [Show full text]
  • Can the Laws of Physics Be Unified? 1St Edition Pdf, Epub, Ebook
    CAN THE LAWS OF PHYSICS BE UNIFIED? 1ST EDITION PDF, EPUB, EBOOK Paul Langacker | 9781400885503 | | | | | Can the Laws of Physics Be Unified? 1st edition PDF Book To test this, you open the hood of the car and examine the oil level. And, whereas a law is a postulate that forms the foundation of the scientific method, a theory is the end result of that process. These analytical skills will help you to excel academically, and they will also help you to think critically in any professional career you choose to pursue. Hawking 28 February Over the centuries, the curiosity of the human race has led us collectively to explore and catalog a tremendous wealth of information. Order a print copy. Such laws are intrinsic to the universe; humans did not create them and so cannot change them. Physical laws in classical mechanics. Newton's laws of motion". You need not be a scientist to use physics. Similarly, the operation of a car's ignition system as well as the transmission of electrical signals through our body's nervous system are much easier to understand when you think about them in terms of basic physics. Physicists use models for a variety of purposes. Answer Key. Leonardo da Vinci , who studied flight and designed many speculative flying machines , understood that "An object offers as much resistance to the air as the air does to the object". Galileo Galilei , however, realised that a force is necessary to change the velocity of a body, i. He goes on to explain field theory, internal symmetries, Yang-Mills theories, strong and electroweak interactions, the Higgs boson discovery, and neutrino physics.
    [Show full text]