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E-raamat: Quantum Mechanics and Its Emergent Macrophysics

  • Formaat: 304 pages
  • Ilmumisaeg: 10-Nov-2020
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9780691221274
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Quantum Mechanics and Its Emergent MacrophysicsSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 10-Nov-2020
  • Kirjastus: Princeton University Press
  • Keel: eng
  • ISBN-13: 9780691221274
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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.

Arvustused

"A clear, well-paced and compact exposition which, through a nice intertwining of physics and mathematics, leaves the reader with a rather complete grasp of the beautiful theoretical construction that goes from the algebraic quantum mechanical framework to thermodynamics, phase transitions and dynamical phase transitions... It offers a road map to a number of central problems in mathematical statistical mechanics. It offers paved access to fascinating physics and mathematics."--Roberto Fernandez, Mathematical Reviews "Sewell's book begins with a self-contained introduction to algebraic quantum theory (especially of infinite systems); and this, together with the fact that Sewell always develops only as much mathematics as he needs for his physics, means that his 300 page book provides a masterly overview of his field."--Jeremy Butterfield, Philosophy of Science

Muu info

A beautifully written book: the physics is well described, the mathematics is precise, and the exposition is concise. Sewell achieves his stated purpose---namely, to offer a panorama of the current state of the problem of how macroscopic phenomena can be interpreted from the laws and structures of microphysics. -- Gerard G. Emch, University of Florida
Preface ix
Notation xi
Part I. The Algebraic Quantum Mechanical Framework and the Description of Order, Disorder and Irreversibility in Macroscopic Systems: Prospectus 1(106)
Introductory Discussion of Quantum Macrophysics
3(4)
The Generalised Quantum Mechanical Framework
7(50)
Observables, States, Dynamics
8(1)
Finite Quantum Systems
8(7)
Uniqueness of the Representation
8(2)
The Generic Model
10(3)
The Algebraic Picture
13(2)
Infinite Systems: Inequivalent Representations
15(3)
The Representation σ(+)
15(2)
The Representation σ(-)
17(1)
Inequivalence of σ(±)
17(1)
Other Inequivalent Representations
18(1)
Operator Algebraic Interlude
18(11)
Algebras: Basic Definitions and Properties
18(3)
States and Representations
21(3)
Automorphisms and Antiautomorphisms
24(2)
Tensor Products
26(1)
Quantum Dynamical Systems
27(1)
Derivations of *-Algebras and Generators of Dynamical Groups
28(1)
Algebraic Formulation of Infinite Systems
29(10)
The General Scheme
29(3)
Construction of the Lattice Model
32(2)
Construction of the Continuum Model
34(5)
The Physical Picture
39(7)
Normal Folia as Local Modifications of Single States
39(1)
Space-translationally Invariant States
39(1)
Primary States have Short Range Correlations
40(1)
Decay of Time Correlations and Irreversibility
41(1)
Global Macroscopic Observables
42(2)
Consideration of Pure Phases
44(1)
Fluctuations and Mesoscopic Observables
45(1)
Open Systems
46(1)
Concluding Remarks
47(10)
Appendix A: Hilbert Spaces
48(9)
On Symmetry, Entropy and Order
57(18)
Symmetry Groups
57(1)
Entropy
58(7)
Classical Preliminaries
58(1)
Finite Quantum Systems
59(3)
Infinite Systems
62(2)
On Entropy and Disorder
64(1)
Order and Coherence
65(7)
Order and Symmetry
65(3)
Coherence
68(1)
Long Range Correlations in G-invariant Mixtures of Ordered Phases
69(1)
Superfluidity and Off-diagonal Long Range Order
70(2)
On Entropy and Order
72(1)
Further Discussion of Order and Disorder
72(3)
Reversibility, Irreversibilty and Macroscopic Causality
75(32)
Microscopic Reversibility
76(3)
Finite Systems
76(2)
Infinite Systems
78(1)
From Systems to Subsystems: Completely Positive Maps, Quantum Dynamical Semigroups and Conditional Expectations
79(4)
Complete Positivity
79(2)
Quantum Dynamical Semigroups
81(1)
Conditional Expectations
82(1)
Induced Dynamical Subsystems
83(1)
Irreversibility
83(3)
Irreversibility, Mixing and Markovian Dynamics
83(3)
Note on Classical Macroscopic Causality
86(21)
Appendix A: Example of a Positive Map that is not Completely Positive
88(1)
Appendix B: Simple Model of Irreversibility and Mixing
89(5)
Appendix C: Simple Model of Irreversibility and Macroscopic Causality
94(1)
The Model
94(4)
Equations of Motion
98(2)
Macroscopic Description of B
100(2)
The Phenomenological Law
102(1)
The Fluctuation Process
103(4)
Part II. From Quantum Statistics to Equilibrium and Nonequilibrium Thermodynamics: Prospectus 107(90)
Thermal Equilibrium States and Phases
109(18)
Introduction
109(2)
Finite Systems
111(2)
Equilibrium, Linear Response Theory and the KMS Conditions
111(1)
Equilibrium and Thermodynamical Stability
112(1)
Resume
112(1)
Infinite Systems
113(10)
The KMS Conditions
113(5)
Thermodynamical Stability Conditions
118(5)
Equilibrium and Metastable States
123(2)
Equilibrium States
123(1)
Metastable States
124(1)
Further Discussion
125(2)
Equilibrium Thermodynamics and Phase Structure
127(22)
Introduction
127(4)
Preliminaries on Convexity
131(4)
Thermodynamic States as Tangents to the Reduced Pressure Function
135(1)
Quantum Statistical Basis of Thermodynamics
136(6)
An Extended Thermodynamics with Order Parameters
142(2)
Concluding Remarks on the Paucity of Thermodynamical Variables
144(5)
Appendix A: Proofs of Propositions 6.4.1 and 6.4.2
145(1)
Appendix B: Functionals q as Space Averages of Locally Conserved Quantum Fields
146(3)
Macrostatistics and Nonequilibrium Thermodynamics
149(48)
Introduction
149(4)
The Quantum Field q(x)
153(2)
The Macroscopic Model, M
155(3)
Relationship between the Classical Field q and the Quantum Field q
158(3)
The Model Mfluct
161(3)
The Linear Regime: Macroscopic Equilibrium Conditions and the Onsager Relations
164(1)
The Nonlinear Regime: Local Equilibrium and Generalized Onsager Relations
165(3)
Further Considerations: Towards a Generalization of the Theory to Galilean Continuum Mechanics
168(29)
Appendix A: Tempered Distributions
170(6)
Appendix B: Classical Stochastic Processes and the Construction of Mfluct as a Classical Markov Field
176(1)
Algebraic Description of Classical Stochastic Processes
176(2)
Classical Gaussian Fields
178(5)
Proof of Propositions 7.5.1 and 7.5.2
183(1)
Appendix C: Equilibrium Correlations and The Static Two-Point Function
183(1)
The Truncated Static Two-Point Function
184(2)
Quantum Statistical Formulation of s''(q)
186(1)
Formulation of π'' via Perturbations of ρθ
187(5)
Proof of Propositions C.3.1 and C.3.2 for Lattice Systems with Finite Range Interactions
192(3)
Pure Crystalline Phases
195(2)
Part III. Superconductive Electrodynamics as a Consequence of Off-diagonal Long Range Order, Gauge Covariance and Thermodynamical Stability: Prospectus 197(42)
Brief Historical Survey of Theories of Superconductivity
199(12)
Off-diagonal Long Range Order and Superconductive Electrodynamics
211(28)
Introduction
211(2)
The General Model
213(5)
ODLRO versus Magnetic Induction
218(3)
Statistical Thermodynamics of the Model and the Meissner Effect
221(5)
The Equilibrium States
221(1)
Thermodynamical Potentials
222(4)
Flux Quantisation
226(3)
Metastability of Supercurrents and Superselection Rules
229(5)
Note on Type II Superconductors
234(2)
Concluding Remarks
236(3)
Appendix A: Vector Potentials Representing Magnetic Fields with Compact Support
236(3)
Part IV. Ordered and Chaotic Structures Far from Equilibrium: Prospectus 239(36)
Schematic Approach to a Theory of Nonequlibrium Phase Transitions, Order and Chaos
241(6)
Laser Model as a Paradigm of Nonequilibrium Phase Structures
247(28)
Introduction
247(1)
The Model
248(8)
The Macroscopic Dynamics
256(4)
The Dynamical Phase Transitions
260(4)
The Microscopic Dynamics
264(5)
A Nonequilibrium Maximum Entropy Principle
269(2)
Concluding Remarks
271(4)
Appendix A: Proof of Lemma 11.5.2 and Proposition 11.5.4
271(4)
References 275(12)
Index 287
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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