Quantum statistical mechanics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
1.1 The density operator and probability......Page 17
1.2 The Gleason theorem and consequences......Page 22
1.3 Calculation of averages of observables......Page 25
Appendix 1A: Gleason theorem......Page 28
References......Page 34
2.2 Harmonic oscillator......Page 35
2.3 Spin one-half and two-level atoms......Page 43
Appendix 2A: the Fokker–Planck equation......Page 50
References......Page 51
3.1 Reduced observables......Page 53
3.2 The Pauli equation......Page 55
3.3 The weak coupling master equation for open systems......Page 58
3.4 Pauli equation: time scaling......Page 62
3.5 Reservoir states: rigorous results and models......Page 69
3.6 The completely positive evolution......Page 70
Appendix 3A: Chapman–Kolmogorov master equation......Page 73
References......Page 75
4.2 Reduced density matrices and the B.B.G.Y.K. hierarchy......Page 77
4.3 Derivation of the quantum Boltzmann equation......Page 79
4.4 Phase space quantum Boltzmann equation......Page 82
4.5 Memory of initial correlations......Page 92
4.6 Quantum Vlasov equation......Page 95
Appendix 4A: phase space distribution functions......Page 96
References......Page 99
5.1 Quantum reversibility......Page 101
5.3 Time irreversibility of the generalized master and Pauli equations......Page 103
5.4 Irreversibility of the quantum operator Boltzmann equation......Page 105
5.5 Reversibility of the quantum Vlasov equation......Page 106
5.6 Completely positive dynamical semigroup: a model......Page 108
Appendix 5A: the quantum time reversal operator......Page 110
References......Page 112
6.2 Macroscopic non-equilibrium thermodynamics......Page 114
6.3 Dissipation and the quantum Boltzmann equation......Page 121
6.4 Negative probability and the quantum H theorem......Page 127
6.5 Entropy and master equations......Page 129
Appendix 6A: quantum recurrence......Page 136
References......Page 137
7 Global equilibrium: thermostatics and the microcanonical ensemble......Page 139
7.1 Boltzmann\'s thermostatic entropy......Page 140
7.2 Thermostatics......Page 141
7.3 Canonical and grand canonical distribution of Gibbs......Page 142
7.4 Equilibrium fluctuations......Page 145
7.5 Negative probability in equilibrium......Page 147
7.6 Non-interacting fermions and bosons......Page 148
7.7 Equilibrium limit theorems......Page 152
References......Page 155
8.1 Introduction......Page 157
8.2 Continuum box model of condensation......Page 158
8.3 Harmonic oscillator trap and condensation......Page 161
8.4 4He: the lambda transition......Page 164
8.5 Fluctuations: comparison of the grand canonical and canonical ensemble......Page 166
8.6 A master equation view of Bose condensation......Page 168
Appendix 8A: exact treatment of condensate traps......Page 171
References......Page 174
9.1 Introduction......Page 175
9.2 Mean field theory and critical indices......Page 176
9.3 Scaling......Page 183
9.4 Renormalization......Page 185
9.5 Renormalization and scaling......Page 188
9.6 Two-dimensional Ising model renormalization......Page 190
References......Page 193
10.1 Introduction......Page 194
10.2 Quantum many-particle dynamics: the event picture......Page 196
10.3 Two-event Boltzmann equation......Page 199
10.4 Some results of the quantum event Boltzmann equation......Page 203
10.5 Relativistic quantum equilibrium event ensembles......Page 207
References......Page 213
11.2 Atomic damping: atomic master equation......Page 215
11.3 Cavity damping: the micromaser: detection......Page 222
11.4 Detection master equation for the cavity field......Page 223
Appendix 11A: the field quantization and interaction......Page 230
References......Page 235
12.2 Entanglements: foundations......Page 237
12.3 Entanglements: Q bits......Page 240
12.4 Entanglement consequences: quantum teleportation, the Bob and Alice story......Page 242
12.6 Entanglement consequences: quantum computation......Page 244
12.7 Decoherence: entanglement destruction......Page 247
12.8 Decoherence correction (error correction)......Page 251
Appendix 12A: entanglement and the Schmidt decomposition......Page 252
References......Page 254
13.1 Introduction......Page 256
13.2 Ideal quantum measurement......Page 257
13.3 Irreversibility: measurement master equations......Page 259
13.4 An open system master equation model for measurement......Page 262
13.5 Stochastic energy based collapse......Page 264
References......Page 267
14.1 Introduction......Page 269
14.2 Quantum Langevin equation......Page 270
14.3 Quantum Langevin equation with measurement......Page 276
References......Page 278
15.1 Introduction......Page 280
15.2 Quantum linear response in the steady state......Page 282
15.3 Linear response, time dependent......Page 285
15.4 Fluctuation and dissipative theorems......Page 288
15.5 Comments and comparisons......Page 293
References......Page 295
16.1 Introduction......Page 297
16.2 One- and two-time quantum Green\'s functions and their properties......Page 298
16.3 Analytic properties of Green\'s functions......Page 300
16.4 Connection to linear response theory......Page 304
16.5 Green\'s function hierarchy truncation......Page 305
16.6 Keldysh time-loop path perturbation theory......Page 313
References......Page 318
17.1 Basic notions and the Wigner–Weisskopf theory......Page 319
17.2 Wigner–Weisskopf method: pole approximation......Page 322
17.3 Wigner–Weisskopf method and Lee–Friedrichs model with a single channel......Page 328
17.4 Wigner–Weisskopf and multichannel decay......Page 334
17.5 Wigner–Weisskopf method with many-channel decay the Lee–Friedrichs model......Page 337
17.6 Gel\'fand triple......Page 348
17.7 Lax–Phillips theory......Page 351
17.8 Application to the Stark model......Page 370
References......Page 378
18.1 Intrinsic theory of irreversibility......Page 381
18.2 Complex Liouvillian eigenvalue method: introduction......Page 382
18.3 Operators and states with diagonal singularity......Page 383
18.4 Super operators and time evolution......Page 385
18.5 Subdynamics and analytic continuation......Page 387
18.6 The Pauli equation revisited......Page 391
References......Page 394
19.1 Introduction......Page 395
19.2 Pauli equation and boundary interaction......Page 396
19.3 Ballistic transport......Page 399
19.4 Green\'s function closed-time path theory to transport......Page 401
References......Page 405
20.1 Introduction to black holes......Page 406
20.2 Equilibrium thermodynamic analogies: the first law......Page 410
20.3 The second law of thermodynamics and black holes......Page 413
20.4 Extended entropy principle for black holes......Page 415
20.5 Acausal evolution: extended irreversible dynamics in black holes......Page 417
References......Page 418
A.2 \"Foundations\" problems......Page 420
A.3 Kinetic dynamics problems......Page 423
A.4 Equilibrium and phase transition problems......Page 425
References......Page 426
Index......Page 427