Book Search:  

 

 
Google full text of our books:

bookjacket

Quantum Mechanics and Its Emergent Macrophysics
Geoffrey Sewell

Book Description | Reviews
Chapter 1 [HTML] or [PDF format]

TABLE OF CONTENTS:

Preface ix
Notation xi

Part I. The Algebraic Quantum Mechanical Framework and the Description of Order, Disorder and Irreversibility in Macroscopic Systems: Prospectus 1

Chapter 1. Introductory Discussion of Quantum Macrophysics 3

Chapter 2. The Generalised Quantum Mechanical Framework 7
2.1. Observables, States, Dynamics 8
2.2. Finite Quantum Systems 8
2.2.1. Uniqueness of the Representation 8
2.2.2. The Generic Model 10
2.2.3. The Algebraic Picture 13
2.3. Infinite Systems: Inequivalent Representations 15
2.3.1. The Representation o-(+) 15
2.3.2. The Representation o(-) 17
2.3.3. Inequivalence of o:(+-) 17
2.3.4. Other Inequivalent Representations 18
2.4. Operator Algebraic Interlude 18
2.4.1. Algebras: Basic Definitions and Properties 18
2.4.2. States and Representations 21
2.4.3. Automorphisms and Antiautomorphisms 24
2.4.4. Tensor Products 26
2.4.5. Quantum Dynamical Systems 27
2.4.6. Derivations of *-Algebras and Generators of Dynamical Groups 28
2.5. Algebraic Formulation of Infinite Systems 29
2.5.1. The General Scheme 29
2.5.2. Construction of the Lattice Model 32
2.5.3. Construction of the Continuum Model 34
2.6. The Physical Picture 39
2.6.1. Normal Folia as Local Modifications of Single States 39
2.6.2. Space-translationally Invariant States 39
2.6.3. Primary States have Short Range Correlations 40
2.6.4. Decay of Time Correlations and Irreversibility 41
2.6.5. Global Macroscopic Observables 42
2.6.6. Consideration of Pure Phases 44
2.6.7. Fluctuations and Mesoscopic Observables 45
2.7. Open Systems 46
2.8. Concluding Remarks 47
Appendix A: filbert Spaces 48

Chapter 3. On Symmetry, Entropy and Order 57
3.1. Symmetry Groups 57
3.2. Entropy 58
3.2.1. Classical Preliminaries 58
3.2.2. Finite Quantum Systems 59
3.2.3. Infinite Systems 62
3.2.4. On Entropy and Disorder 64
3.3. Order and Coherence 65
3.3.1 Order and Symmetry 65
3.3.2. Coherence 68
3.3.3. Long Range Correlations in G-invariant Mixtures of Ordered Phases 69
3.3.4 Superfluidity and Off-diagonal Long Range Order 70
3.3.5. On Entropy and Order 72
3.4. Further Discussion of Order and Disorder 72

Chapter 4. Reversibility, Irreversibilty and Macroscopic Causality 75
4.1. Microscopic Reversibility 76
4.1.1. Finite Systems 76
4.1.2. Infinite Systems 78
4.2. From Systems to Subsystems: Completely Positive Maps, Quantum Dynamical Semigroups and Conditional Expectations 79
4.2.1. Complete Positivity 79
4.2.2. Quantum Dynamical Semigroups 81
4.2.3. Conditional Expectations 82
4.3. Induced Dynamical Subsystems 83
4.4. Irreversibility 83
4.4.1. Irreversibility, Mixing and Markovian Dynamics 83
4.5. Note on Classical Macroscopic Casuality 86

Appendix A: Example of a Positive Map that is not Completely Posistive 88
Appendix B. Simple Model of Irrversibilty and Mixing 89
Appendix C. Simple Model of Irreversibilty and Macroscopic Casuality 94
C.1. The Model 94
C.2. Equations of Motion 98
C.3. Macroscopic Description of B 100
C.4. The Phenomenological Law 102
C.5. The Fluctuation Process 103

Part II. From Quantum Statistics to Equilibrium and Nonequilibrium Thermodynamics: Prospectus 107

Chapter 5. Thermal Equilibrium States and Phases 109
5.1. Introduction 109
5.2. Finite Systems 11l
5.2.1. Equilibrium, Linear Response Theory and the KMS Conditions 111
5.2.2. Equilibrium and Thermodynamical Stability 112
5.2.3. Resume 112
5.3. Infinite Systems 113
5.3.1. The KMS Conditions 113
5.3.2. Thermodynamical Stability Conditions 118
5.4. Equilibrium and Metastable States 123
5.4.1. Equilibrium States 123
5.4.2. Metastable States 124
5.5. Further Discussion 125

Chapter 6. Equilibrium Thermodynamics and Phase Structure 127
6.1. Introduction 127
6.2. Preliminaries on Convexity 131
6.3. Thermodynamic States as Tangents to the Reduced Pressure Function 135
6.4. Quantum Statistical Basis of Thermodynamics 136
6.5. An Extended Thermodynamics with Order Parameters 142
6.6. Concluding Remarks on the Paucity of Thermodynamical Variables 144

Appendix A: Proofs of Propositions 6.4.1 and 6.4.2 145
Appendix B: Functionals q as Space Averages of Locally Conserved Quantum Fields 146

Chapter 7. Macrostatistics and Nonequilibrium Thermodynamics 149
7.1. Introduction 149
7.2. The Quantum Field q(x) 153
7.3. The Macroscopic Model, M 155
7.4. Relationship between the Classical Field q and the Quantum Field q 158
7.5. The Model M(flunt) 161
7.6. The Linear Regime: Macroscopic Equilibrium Conditions and the Onsager Relations 164
7.7. The Nonlinear Regime: Local Equilibrium and Generalized Onsager Relations 165
7.8. Further Considerations: Towards a Generalization of the Theory to Galilean Continuum Mechanics 168

Appendix A: Tempered Distributions 170
Appendix B: Classical Stochastic Processes and the Construction of M(flunt) as a Classical Markov Field 176
B.1. Algebraic Description of Classical Stochastic Processes 176
B.2. Classical Gaussian Fields 178
B.3. Proof of Propositions 7.5.1 and 7.5.2 183
Appendix C: Equilibrium Correlations and The Static Two-Point Function 183
C.1. The Truncated Static Two-Point Function 184
C.2. Quantum Statistical Formulation of s"(q) 186
C.3. Formulation of n" via Perturbations of po 187
C.4. Proof of Propositions C.3.1 and C.3.2 for Lattice Systems with Finite Range Interactions 192
C.5. Pure Crystalline Phases 195

Part III. Superconductive Electrodynamics as a Consequence of Off-diagonal Long Range Order, Gauge Covariance and Thermodynamical Stability: Prospectus 197
,p> Chapter 8. Brief Historical Survey of Theories of Superconductivity 199
Chapter 9. Off-diagonal Long Range Order and Superconductive Electrodynamics 211
9.1. Introduction 211
9.2. The General Model 213
9.3. ODLRO versus Magnetic Induction 218
9.4. Statistical Thermodynamics of the Model and the Meissner Effect 221
9.4.1 The Equilibrium States 221
9.4.2 Thermodynamical Potentials 222
9.5. Flux Quantisation 226
9.6. Metastability of Supercurrents and Superselection Rules 229
9.7. Note on Type II Superconductors 234
9.8. Concluding Remarks 236
Appendix A: Vector Potentials Representing Magnetic Fields with Compact Support 236

Part IV. Ordered and Chaotic Structures Far from Equilibrium: Prospectus 239

Chapter 10. Schematic Approach to a Theory of Nonequlibrium Phase Transitions, Order and Chaos 241
Chapter 11. Laser Model as a Paradigm of Nonequilibrium Phase Structures 247
11.1. Introduction 247
11.2. The Model 248
11.3. The Macroscopic Dynamics 256
11.4. The Dynamical Phase Transitions 260
11.5. The Microscopic Dynamics 264
11.6. A Nonequilibrium Maximum Entropy Principle 269
11.7. Concluding Remarks 271
Appendix A: Proof of Lemma 11.5.2 and Proposition 11.5.4 271

References 275
Index 287

Return to Book Description

File created: 4/17/2014

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Sample Chapters
Subjects
Series
Catalogs
Textbooks
For Reviewers
Class Use
Rights
Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
Princeton APPS
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share