Decoherence and the Appearance of a Classical World in Quantum Theory

by Joos, Erich; Zeh, H. D.; Kiefer, Claus; Giulini, Domenico; Kupsch, Joachim; Stamatescu, I. O.; Joos, Erich

• ISBN13: 9783540003908
• ISBN10: 3540003908
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-07-01
• Publisher: Springer Verlag

Summary

This book describes the phenomena that arise from the interaction between quantum systems and their environment. Since the first edition appeared in 1996, the concepts of decoherence have become firmly established experimentally and are now widely used in the literature. Its major consequences are the emergence of 'classicality', superselection rules, the border line between microscopic and macroscopic behavior, the emergence of classical spacetime, and the appearance of quantum jumps. Most of the new developments in this rapidly evolving field are discussed in this second edition: chaos theory, quantum information, neuroscience, primordial fluctuations in cosmology, black holes and string theory, experimental tests, and interpretational issues. While the major part of the book is concerned with environmental decoherence derived from a universal Schroedinger equation, later chapters address complementary or competing approaches, such as consistent histories, open syste

Table of Contents

Introduction	p. 1
Basic Concepts and Their Interpretation	p. 7
The Phenomenon of Decoherence	p. 7
Superpositions	p. 7
Superselection Rules	p. 11
Decoherence by "Measurements"	p. 13
Observables as a Derived Concept	p. 17
The Measurement Problem	p. 21
Density Matrix, Coarse Graining, and "Events"	p. 33
Conclusions	p. 40
Decoherence Through Interaction with the Environment	p. 41
The General Mechanisms of Decoherence	p. 47
Dynamics of Quantum Correlations	p. 47
Scattering Processes	p. 55
Environment-Induced Superselection Rules	p. 57
Localization of Objects	p. 62
Localization Through Ideal Measurements	p. 64
Spatial Decoherence	p. 64
Equation of Motion	p. 70
Decohering Wave Packets	p. 75
More General Recoil-Free Decoherence	p. 78
Decoherence and Dissipation	p. 79
Quantum Brownian Motion	p. 79
Ehrenfest Theorems	p. 87
Decoherence Versus Friction	p. 89
Wigner Function Description of Decoherence	p. 90
Molecular Structure	p. 99
Decoherence in the Brain	p. 107
Dynamical Consequences	p. 109
The Quantum Zeno Effect	p. 110
Phenomenological Description	p. 111
An Experimental Test	p. 118
Models for the Quantum Zeno Effect	p. 122
Master Equations	p. 126
Pauli Equation	p. 126
Lindblad's Form of Master Equations	p. 133
Dynamical Stability of States	p. 135
Sensitivity to the Presence of an Environment	p. 136
Decoherence and Quantum Computation	p. 145
Quantum Nondemolition Measurements	p. 147
Decoherence and Quantum Chaos	p. 149
Classical Versus Quantum Chaos	p. 149
Example: The Kicked Rotator	p. 152
Quantum (?) Chaos in the Solar System	p. 156
Decoherence Through Chaotic Environments	p. 159
Interpretational Issues	p. 161
Null Measurements, Histories and Quantum Jumps	p. 161
Quantum "Information" and Teleportation	p. 172
True, False, and Fake Decoherence	p. 175
Decoherence in Quantum Field Theory and Quantum Gravity	p. 181
Decoherence in Quantum Electrodynamics	p. 182
"Measurement" of Charges by Fields	p. 182
"Measurement" of Electromagnetic Fields by Charges	p. 188
Decoherence and the Gravitational Field	p. 192
Emergence of Classical Spacetime	p. 192
The Formalism of Quantum Cosmology	p. 196
Decoherence in Quantum Cosmology	p. 199
Classicality of Primordial Fluctuations in the Early Universe	p. 209
Black Holes, Wormholes, and String Theory	p. 218
Consistent Histories and Decoherence	p. 227
Influence Functional and Its Application to Quantum Brownian Motion	p. 229
Definition and Properties of Consistent Histories	p. 238
Reduced Density Matrix and Decoherence	p. 247
Consistent Histories, Arrow of Time, and Quantum Gravity	p. 251
Superselection Rules and Symmetries	p. 259
States, Observables, and Superselection Rules	p. 261
Spaces of States	p. 262
Spaces of Observables	p. 267
Superselection Rules	p. 275
Symmetries and Superselection Rules	p. 278
Symmetries	p. 279
Superselection Rules from Symmetries	p. 284
An Example: The Univalence Superselection Rule	p. 285
Discussion and Caveats	p. 287
Physical Symmetries Versus Gauge Transformations	p. 289
Configuration Spaces and Spaces of State	p. 289
Symmetries and Redundant State Spaces	p. 292
Symmetries, Redundancies, and Superselection Rules	p. 297
Superselection Rules in Field Theory	p. 303
Charge and Asymptotic Flux-Distribution in QED	p. 304
Poincare Charges in General Relativity	p. 310
Decoherence and Charge Superselection Rules	p. 312
Open Quantum Systems	p. 317
Reduced Dynamics	p. 319
Projection Methods	p. 321
Generalized Master Equations	p. 327
Markov Approximation and Semigroups	p. 330
Quantum Stochastic Processes	p. 333
Induced Superselection Sectors	p. 339
General Considerations	p. 339
Hamiltonian Models of Decoherence	p. 341
The Araki-Zurek Models	p. 343
Particle Coupled to a Massless Boson Field	p. 345
Models with Scattering	p. 347
Heisenberg Picture	p. 348
Mathematical Supplement	p. 350
Spaces of Linear Operators	p. 350
Complete Positivity	p. 354
Entropy Inequalities	p. 355
Stochastic Collapse Models	p. 357
The Question of State Vector Reduction	p. 357
Two Points of View	p. 357
Decoherence, Collapse, Measurement	p. 358
Various Approaches to Collapse	p. 363
Spontaneous Collapse Models	p. 369
The Dynamical Collapse Hypothesis	p. 369
Spontaneous Localization by a Jump Process	p. 370
Continuous Spontaneous Localization	p. 373
Spontaneous Localization, Quantum State Diffusion and Decoherence	p. 378
Related Concepts and Methods	p. 383
Phase Averaging in Ensembles ("Dephasing")	p. 383
Ergodicity and Irreversible Amplification	p. 385
Dressing of States	p. 387
Symmetry Breaking and Collective Motion	p. 388
Equation of Motion of a Mass Point	p. 395
Solutions for the Equation of Motion	p. 399
Gaussian Density Matrices	p. 399
Green Functions	p. 402
Some Derived Quantities	p. 403
Elementary Properties of Composite Systems in Quantum Mechanics	p. 407
Quantum Correlations	p. 415
Hamiltonian Formulation of Quantum Mechanics	p. 419
Galilean Symmetry of Non-Relativistic Quantum Mechanics	p. 425
Stochastic Processes	p. 433
Random Variables and Distributions	p. 433
Markov Chains	p. 434
Stochastic Processes	p. 436
The Fokker-Planck Equation	p. 437
Stochastic Differential Equations	p. 439
References	p. 445
Table of Contents provided by Ingram. All Rights Reserved.