Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Graduate Texts)

Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity; the physical systems discussed include liquid 4-He, the BEC alkali gases, "classical" superconductors, superfluid 3-He, "exotic" superconductors and the recently stabilized Fermi alkali gases.The book should be accessible to beginning graduate students in physics or advanced undergraduates. Contents......Page 10 Preface......Page 6 List of symbols......Page 12 1 Quantum liquids......Page 18 1.1 Indistinguishability and the symmetry of the many-body wave function......Page 20 1.2 The Fermi–Dirac and Bose–Einstein distributions: BEC in a noninteracting gas......Page 25 1.3 Cooper pairing......Page 30 1.4 The experimental systems......Page 32 1.5 Superconductivity and superfluidity: basic phenomenology......Page 37 Appendix......Page 43 2.1 Definition of BEC in an interacting system......Page 48 2.2 The order parameter and the superfluid velocity; alternative definitions of BEC......Page 51 2.3 Why should BEC occur in an interacting system? When does it (not)?......Page 57 2.4 Pseudo-BEC in a Fermi system (Cooper pairing)......Page 63 2.5 The consequences of BEC: preview of coming attractions......Page 70 2.6 Fragmented BEC......Page 77 Appendices......Page 80 3 Liquid [sup(4)]He......Page 88 3.1 Anomalous properties of the He-II phase......Page 89 3.2 Direct evidence for BEC in He-II......Page 90 3.3 The two-fluid model of He-II: static effects......Page 93 3.4 The two-fluid model: dynamical effects......Page 100 3.5 Quantized vortices, phase slip and the Josephson effect......Page 108 3.6 The excitation spectrum of liquid He-II......Page 115 3.7 Microscopic theories of He-II......Page 119 4.1 The atoms: structure, trapping, and diagnostics......Page 130 4.2 s-wave scattering and effective interaction......Page 135 4.3 The Gross–Pitaevskii equation: some simple applications......Page 140 4.4 The Bogoliubov approximation......Page 148 4.5 Coherence and interference in dilute alkali Bose gases......Page 151 4.6 Optical lattices......Page 162 4.7 Signatures of superfluidity in the BEC alkali gases......Page 167 Appendix......Page 174 5.1 The normal state......Page 182 5.2 The effective electron–electron interaction......Page 187 5.3 The Cooper instability......Page 192 5.4 BCS theory at T = 0......Page 195 5.5 Excited states and finite-temperature BCS theory......Page 203 5.6 The two-fluid model for superconductors: the Meissner effect......Page 207 5.7 The Ginzburg–Landau theory......Page 215 5.8 Generalizations of BCS: the “non-pair-breaking” case......Page 225 5.9 Pair-breaking effects......Page 233 5.10 The Josephson effect......Page 240 Appendix......Page 245 6.1 The normal phase of liquid [sup(3)]He......Page 268 6.2 Anisotropic Cooper pairing......Page 271 6.3 Generalized Ginzburg–Landau approach: spin fluctuation feedback......Page 277 6.4 Spontaneously broken spin–orbit symmetry and spin dynamics......Page 282 6.5 Supercurrents, textures and defects......Page 289 7.1 Introduction......Page 300 7.2 The cuprates: composition, structure, and phase diagram......Page 301 7.3 The cuprates: principal experimental properties......Page 312 7.4 Normal state at optimal doping......Page 313 7.5 The “pseudogap” regime......Page 319 7.6 Superconducting state......Page 321 7.7 Some preliminary comments on the experimental data......Page 330 7.8 What do we know for sure about cuprate superconductivity?......Page 331 7.9 The cuprates: questions and ideas......Page 343 7.10 Novel consequences of Cooper pairing in the cuprates......Page 353 Appendices......Page 363 8.1 Noncuprate “exotic” superconductors......Page 366 8.2 Liquid [sup(3)]He in aerogel......Page 372 8.3 Supersolids......Page 375 8.4 Fermi alkali gases: the BEC-BCS crossover......Page 381 Appendix......Page 388 Bibliography......Page 390 B......Page 398 D......Page 399 G......Page 400 J......Page 401 N......Page 402 P......Page 403 S......Page 404 Z......Page 405 The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.--Werner HeisenbergThat God would choose to play dice with the world is something I cannot believe.--Albert EinsteinNothing exists until it is measured.--Neils BohrThe remarkable story of a startling scientific idea that ignited a battle among the greatest minds of the twentieth century and profoundly influenced intellectual inquiry in fields ranging from physics to literary criticism, anthropology and journalismIn 1927, the young German physicist Werner Heisenberg challenged centuries of scientific understanding when he introduced what came to be known as "the uncertainty principle." Building on his own radical innovations in quantum theory, Heisenberg proved that in many physical measurements, you can obtain one bit of information only at the price of losing another. Heisenberg's principle implied that scientific quantities/concepts do not have absolute, independent meaning, but acquire meaning only in terms of the experiments used to measure them. This proposition, undermining the cherished belief that science could reveal the physical world with limitless detail and precision, placed Heisenberg in direct opposition to the revered Albert Einstein. The eminent scientist Niels Bohr, Heisenberg's mentor and Einstein's long-time friend, found himself caught between the two.Uncertainty chronicles the birth and evolution of one of the most significant findings in the history of science, and portrays the clash of ideas and personalities it provoked. Einstein was emotionally as well as intellectually determined to prove the uncertainty principle false. Heisenberg represented a new generation of physicists who believed that quantum theory overthrew the old certainties; confident of his reasoning, Heisenberg dismissed Einstein's objections. Bohr understood that Heisenberg was correct, but he also recognized the vital necessity of gaining Einstein's support as the world faced the shocking implications of Heisenberg's principle. The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. Werner Heisenberg That God would choose to play dice with the world is something I cannot believe. Albert Einstein Nothing exists until it is measured. Neils Bohr The remarkable story of a startling scientific idea that ignited a battle among the greatest minds of the twentieth century and profoundly influenced intellectual inquiry in fields ranging from physics to literary criticism, anthropology and journalism In 1927, the young German physicist Werner Heisenberg challenged centuries of scientific understanding when he introduced what came to be known as the uncertainty principle. Building on his own radical innovations in quantum theory, Heisenberg proved that in many physical measurements, you can obtain one bit of information only at the price of losing another. Heisenbergs principle implied that scientific quantities/concepts do not have absolute, independent meaning, but acquire meaning only in terms of the experiments used to measure them. This proposition, undermining the cherished belief that science could reveal the physical world with limitless detail and precision, placed Heisenberg in direct opposition to the revered Albert Einstein. The eminent scientist Niels Bohr, Heisenbergs mentor and Einsteins long-time friend, found himself caught between the two. Uncertainty chronicles the birth and evolution of one of the most significant findings in the history of science, and portrays the clash of ideas and personalities it provoked. Einsteinwas emotionally as well as intellectually determined to prove the uncertainty principle false. Heisenberg represented a new generation of physicists who believed that quantum theory overthrew the old certainties; confident of his reasoning, Heisenberg dismissed Einsteins objections. Bohr understood that Heisenberg was correct, but he also recognized the vital necessity of gaining Einsteins support as the world faced the shocking implications of Heisenbergs principle. Max Jammer's Concepts Of Simultaneity Presents A Comprehensive, Accessible Account Of The Historical Development Of An Important And Controversial Concept--which Played A Critical Role In Initiating Modern Theoretical Physics--from The Days Of Egyptian Hieroglyphs Through To Einstein's Work In 1905, And Beyond. Beginning With The Use Of The Concept Of Simultaneity In Ancient Egypt And In The Bible, The Study Discusses Its Role In Greek And Medieval Philosophy As Well As Its Significance In Newtonian Physics And In The Ideas Of Leibniz, Kant, And Other Classical Philosophers. The Central Theme Of Jammer's Presentation Is A Critical Analysis Of The Use Of This Concept By Philosophers Of Science, Like Poincare, And Its Significant Role In Inaugurating Modern Theoretical Physics In Einstein's Special Theory Of Relativity. Particular Attention Is Paid To The Philosophical Problem Of Whether The Notion Of Distant Simultaneity Presents A Factual Reality Or Only A Hypothetical Convention. The Study Concludes With An Analysis Of Simultaneity's Importance In General Relativity And Quantum Mechanics.--publisher's Website. 1. Terminological Preliminaries -- 2. The Concept Of Simultaneity In Antiquity -- 3. Medieval Conceptions Of Simultaneity -- 4. The Concept Of Simultaneity In The Sixteenth And Seventeenth Centuries -- 5. The Concept Of Simultaneity In Classical Physics -- 6. The Transition To The Relativistic Conception Of Simultaneity -- 7. Simultaneity In The Special Theory Of Relativity -- 8. The Reception Of The Relativistic Conception Of Simultaneity -- 9. The Conventionality Thesis -- 10. The Promulgation Of The Conventionality Thesis -- 11. Symmetry And Transitivity Of Simultaneity -- 12. Arguments Against The Conventionality Thesis -- 13. Clock Transport Synchrony -- 14. Recent Debates On The Conventionality Of Simultaneity. Max Jammer. Includes Bibliographical References And Index. Max Jammer's Concepts of Simultaneity presents a comprehensive, accessible account of the historical development of an important and controversial concept—which played a critical role in initiating modern theoretical physics—from the days of Egyptian hieroglyphs through to Einstein's work in 1905, and beyond. Beginning with the use of the concept of simultaneity in ancient Egypt and in the Bible, the study discusses its role in Greek and medieval philosophy as well as its significance in Newtonian physics and in the ideas of Leibniz, Kant, and other classical philosophers. The central theme of Jammer's presentation is a critical analysis of the use of this concept by philosophers of science, like Poincaré, and its significant role in inaugurating modern theoretical physics in Einstein's special theory of relativity. Particular attention is paid to the philosophical problem of whether the notion of distant simultaneity presents a factual reality or only a hypothetical convention. The study concludes with an analysis of simultaneity's importance in general relativity and quantum mechanics. The remarkable story of a startling scientific idea that ignited a battle among the greatest minds of the twentieth century and profoundly influenced intellectual inquiry in fields ranging from physics to literary criticism, anthropology and journalism. In 1927, young German physicist Werner Heisenberg challenged centuries of scientific understanding when he introduced what came to be known as "the uncertainty principle." Heisenberg proved that in many physical measurements, you can obtain one bit of information only at the price of losing another. This proposition, undermining the cherished belief that science could reveal the physical world with limitless detail and precision, placed Heisenberg in direct opposition to the revered Albert Einstein. Niels Bohr, Heisenberg's mentor and Einstein's long-time friend, found himself caught between the two. Bohr understood that Heisenberg was correct, but he also recognized the vital necessity of gaining Einstein's support as the world faced the shocking implications of Heisenberg's principle.--From publisher description Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases,'classical'superconductors, superfluid 3-He,'exotic'superconductors and the recently stabilized Fermi alkali gases. The book should be accessible to beginning graduate students in physics or advanced undergraduates. ## Abstract Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way. Their consequences in condensed matter systems are also explored. Eschewing advanced formal methods, the book uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases, “classical” superconductors, superfluid 3-He, “exotic” superconductors, and the recently stabilized Fermi alkali gases. Introducing The Related Phenomena Of Bose Condensation And Cooper Pairing, In Which A Very Large Number Of Single Particles Or Pairs Of Particles Are Forced To Behave In Exactly The Same Way, This Book Explores Their Consequences In Condensed Matter Systems, Eschewing Advanced Formal Methods. 1 Quantum Liquids -- 2 Bec: Its Definition, Origin, Occurrence, And Consequences -- 3 Liquid 4he -- 4 The Bose Alkali Gases -- 5 Classical Superconductivity -- 6 Superfluid 3he -- 7 Cuprate Superconductivity -- 8 Miscellaneous Topics A.j. Leggett. Includes Bibliographical References (p. 373-379) And Index. Max Jammer's Simultaneity offers a comprehensive and fully documented account of how the concept of simultaneity evolved throughout the centuries, from its use in ancient Egypt and the Bible, to its presence in Pre-Socratic, Aristotelian, Hellenistic and medieval philosophy, to its significance in Newtonian physics and in the philosophies of Leibniz and Kant. He discusses its function in the special and general theories of relativity and quantum mechanics, and provides insight into the ongoing present-day discourse on the conventionality thesis of distant simultaneity