Quantum Mechanics and Its Emergent Macrophysics

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Princeton University Press, 2002 - Science - 292 pages
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The quantum theory of macroscopic systems is a vast, ever-developing area of science that serves to relate the properties of complex physical objects to those of their constituent particles. Its essential challenge is that of finding the conceptual structures needed for the description of the various states of organization of many-particle quantum systems. In this book, Geoffrey Sewell provides a new approach to the subject, based on a "macrostatistical mechanics," which contrasts sharply with the standard microscopic treatments of many-body problems.

Sewell begins by presenting the operator algebraic framework for the theory. He then undertakes a macrostatistical treatment of both equilibrium and nonequilibrium thermodynamics, which yields a major new characterization of a complete set of thermodynamic variables and a nonlinear generalization of the Onsager theory. The remainder of the book focuses on ordered and chaotic structures that arise in some key areas of condensed matter physics. This includes a general derivation of superconductive electrodynamics from the assumptions of off-diagonal long-range order, gauge covariance, and thermodynamic stability, which avoids the enormous complications of the microscopic treatments. Sewell also unveils a theoretical framework for phase transitions far from thermal equilibrium. Throughout, the mathematics is kept clear without sacrificing rigor.

Representing a coherent approach to the vast problem of the emergence of macroscopic phenomena from quantum mechanics, this well-written book is addressed to physicists, mathematicians, and other scientists interested in quantum theory, statistical physics, thermodynamics, and general questions of order and chaos.

  

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Contents

The generalised quantum mechanical framework
7
21 OBSERVABLES STATES DYNAMICS
8
222 The Generic Model
10
223 THE ALGEBRAIC PICTURE
13
INEQUIVALENT REPRESENTATIONS
15
232 The Representation a
17
234 Other Inequivalent Representations
18
242 States and Representations
21
53 INFINITE SYSTEMS
113
532 Thermodynamical Stability Conditions
118
541 Equilibrium States
123
542 Metastable States
124
55 FURTHER DISCUSSION
125
Equilibrium thermodynamics and phase structure 61 INTRODUCTION
127
62 PRELIMINARIES ON CONVEXITY6
131
63 THERMODYNAMIC STATES AS TANGENTS TO THE REDUCED PRESSURE FUNCTION
135

243 Automorphisms and Antiautomorphisms
24
244 Tensor Products
26
245 Quantum Dynamical Systems
27
246 Derivations of Algebras and Generators of Dynamical Groups BR
28
25 ALGEBRAIC FORMULATION OF INFINITE SYSTEMS
29
252 Construction of the Lattice Model cf St Rol
32
253 Construction of the Continuum Model cf HHW DS Se4
34
26 THE PHYSICAL PICTURE
39
263 Primary States have Short Range Correlations
40
264 Decay of Time Correlations and Irreversibility
41
265 Global Macroscopic Observables cf He
42
266 Consideration of Pure Phases
44
267 Fluctuations and Mesoscopic Observables cf GW
45
27 OPEN SYSTEMS
46
28 CONCLUDING REMARKS
47
HILBERT SPACES
48
On symmetry entropy and order
57
321 Classical Preliminaries SW Khl
58
322 Finite Quantum Systems
59
323 Infinite Systems
62
324 On Entropy and Disorder
64
33 ORDER AND COHERENCE
65
332 Coherence
68
333 Long Range Correlations in Ginvariant Mixtures of Ordered Phases
69
334 Superfluidity and Offdiagonal Long Range Order
70
335 On Entropy and Order
72
Reversibility irreversibilty and macroscopic causality
75
411 Finite Systems
76
412 Infinite Systems
78
COMPLETELY POSITIVE MAPS QUANTUM DYNAMICAL SEMIGROUPS AND CONDITIONAL EXPECTATIONS 421 Complete Positivity
79
422 Quantum Dynamical Semigroups
81
423 Conditional Expectations
82
43 INDUCED DYNAMICAL SUBSYSTEMS
83
45 NOTE ON CLASSICAL MACROSCOPIC CAUSALITY From Quantum Stochastics to Classical Determinism
86
EXAMPLE OF A POSITIVE MAP THAT IS NOT COMPLETELY POSITIVE
88
SIMPLE MODEL OF IRREVERSIBILITY AND MIXING
89
SIMPLE MODEL OF IRREVERSIBILITY AND MACROSCOPIC CAUSALITY
94
C2 EQUATIONS OF MOTION
98
C3 Macroscopic Description of B
100
C4 The Phenomenological Law
102
C5 The Fluctuation Process
103
From quantum statistics to equilibrium and nonequilibrium thermodynamics prospectus
107
Thermal equilibrium states and phases 51 INTRODUCTION
109
52 FINITE SYSTEMS
111
522 Equilibrium and Thermodynamical Stability
112
64 QUANTUM STATISTICAL BASIS OF THERMODYNAMICS
136
65 AN EXTENDED THERMODYNAMICS WITH ORDER PARAMETERS
142
66 CONCLUDING REMARKS ON THE PAUCITY OF THERMODYNAMICAL VARIABLES
144
PROOFS OF PROPOSITIONS 641 AND 642
145
FUNCTIONALS q AS SPACE AVERAGES OF LOCALLY CONSERVED QUANTUM FDZLDS
146
Macrostatistics and nonequilibrium thermodynamics 71 INTRODUCTION
149
72 THE QUANTUM FIELD qx
153
73 THE MACROSCOPIC MODEL M
155
74 RELATIONSHIP BETWEEN THE CLASSICAL FIELD q AND THE QUANTUM FIELD q
158
t
161
MACROSCOPIC EQUILIBRIUM CONDITIONS AND THE ONSAGER RELATIONS
164
LOCAL EQUILIBRIUM AND GENERALISED ONSAGER RELATIONS
166
TOWARDS A GENERALISATION OF THE THEORY TO GALILEAN CONTINUUM MECHANICS
168
TEMPERED DISTRIBUTIONS
170
CLASSICAL STOCHASTIC PROCESSES AND THE CONSTRUCTION OF 31nutt AS A CLASSICAL MARKOV FIELD
176
B2 CLASSICAL GAUSSIAN FIELDS
178
B3 Proof of Propositions 751 and 752
183
CI The Truncated Static TwoPoint Function
184
C2 Quantum Statistical Formulation of sq
186
C3 Formulation of T via Perturbations of pe
187
C4 PROOF OF PROPOSITIONS C31 AND C32 FOR LATTICE SYSTEMS WITH FINITE RANGE INTERACTIONS
192
C5 Pure Crystalline Phases
195
Superconductive electrodynamics as a consequence of offdiagonal long range order gauge covariance and thermodynamical stability prospectus
197
Brief historical survey of theories of superconductivity
199
Offdiagonal long range order and superconductive electrodynamics 91 INTRODUCTION
211
92 THE GENERAL MODEL
213
93 ODLRO VERSUS MAGNETIC INDUCTION
218
94 STATISTICAL THERMODYNAMICS OF THE MODEL AND THE MEISSNER EFFECT
221
942 Thermodynamical Potentials
222
95 FLUX QUANTISATION
226
96 METASTABILITY OF SUPERCURRENTS AND SUPERSELECTION RULES
229
97 NOTE ON TYPE II SUPERCONDUCTORS
234
98 CONCLUDING REMARKS
236
Ordered and chaotic structures far from equilibrium prospectus
239
Schematic approach to a theory of nonequlibrium phase transitions order and chaos
241
Laser model as a paradigm of nonequilibrium phase structures 111 INTRODUCTION
247
112 THE MODEL
248
113 THE MACROSCOPIC DYNAMICS
256
114 THE DYNAMICAL PHASE TRANSITIONS
260
115 THE MICROSCOPIC DYNAMICS
264
116 A NONEQUILIBRIUM MAXIMUM ENTROPY PRINCIPLE
269
117 CONCLUDING REMARKS
271
References
275
Index
287
Copyright

Common terms and phrases

Popular passages

Page 275 - Multiple time analyticity of a quantum statistical state satisfying the KMS boundary condition.
Page 275 - AFL] L. Accardi, A. Frigerio and JT Lewis: Quantum stochastic processes, Publ. RIMS 18, 97-133, 1982.
Page ix - Accordingly, it appears natural to pursue an approach to the theory of its emergence from quantum mechanics that is centred on macroscopic observables and certain general features of quantum structures, independently of microscopic details.
Page 283 - GL Sewell: Unbounded local observables in quantum statistical mechanics, J. Math. Phys. 11, 1868-1884, 1970.
Page 285 - Neutral fermion, charge-e boson excitations in the resonating-valence-bond state and superconductivity in L compounds, Phys.
Page x - In accordance with these concepts, the book is divided into four parts. Part I consists of a single chapter in which the foregoing premises are stated and an attempt is made to justify them.

References to this book

Philosophy of Physics: Part B.

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About the author (2002)

Geoffrey Sewell is Professor of Mathematical Physics at Queen Mary, University of London. His previous book, "Quantum Theory of Collective Phenomena," is a classic in the field.

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