| Preface | p. xi |
| Foundations of quantum statistical mechanics | p. 1 |
| The density operator and probability | p. 1 |
| The Gleason theorem and consequences | p. 6 |
| Calculation of averages of observables | p. 9 |
| Gleason theorem | p. 12 |
| References | p. 18 |
| Elementary examples | p. 19 |
| Introduction | p. 19 |
| Harmonic oscillator | p. 19 |
| Spin one-half and two-level atoms | p. 27 |
| the Fokker-Planck equation | p. 34 |
| References | p. 35 |
| Quantum statistical master equation | p. 37 |
| Reduced observables | p. 37 |
| The Pauli equation | p. 39 |
| The weak coupling master equation for open systems | p. 42 |
| Pauli equation: time scaling | p. 46 |
| Reservoir states: rigorous results and models | p. 53 |
| The completely positive evolution | p. 54 |
| Chapman-Kolmogorov master equation | p. 57 |
| References | p. 59 |
| Quantum kinetic equations | p. 61 |
| Introduction | p. 61 |
| Reduced density matrices and the B.B.G.Y.K. hierarchy | p. 61 |
| Derivation of the quantum Boltzmann equation | p. 63 |
| Phase space quantum Boltzmann equation | p. 66 |
| Memory of initial correlations | p. 76 |
| Quantum Vlasov equation | p. 79 |
| Phase space distribution functions | p. 80 |
| References | p. 83 |
| Quantum irreversibility | p. 85 |
| Quantum reversibility | p. 85 |
| Master equation and irreversibility | p. 87 |
| Time irreversibility of the generalized master and Pauli equations | p. 87 |
| Irreversibility of the quantum operator Boltzmann equation | p. 89 |
| Reversibility of the quantum Vlasov equation | p. 90 |
| Completely positive dynamical semigroup: a model | p. 92 |
| the quantum time reversal operator | p. 94 |
| References | p. 96 |
| Entropy and dissipation: the microscopic theory | p. 98 |
| Introduction | p. 98 |
| Macroscopic non-equilibrium thermodynamics | p. 98 |
| Dissipation and the quantum Boltzmann equation | p. 105 |
| Negative probability and the quantum $$ theorem | p. 111 |
| Entropy and master equations | p. 113 |
| quantum recurrence | p. 120 |
| References | p. 121 |
| Global equilibrium: thermostatics and the microcanonical ensemble | p. 123 |
| Boltzmann's thermostatic entropy | p. 124 |
| Thermostatics | p. 125 |
| Canonical and grand canonical distribution of Gibbs | p. 126 |
| Equilibrium fluctuations | p. 129 |
| Negative probability in equilibrium | p. 131 |
| Non-interacting fermions and bosons | p. 132 |
| Equilibrium limit theorems | p. 136 |
| References | p. 139 |
| Bose-Einstein ideal gas Condensation | p. 141 |
| Introduction | p. 141 |
| Continuum box model of condensation | p. 142 |
| Harmonic oscillator trap and condensation | p. 145 |
| 4He: the transition | p. 148 |
| Fluctuations: comparison of the grand canonical and canonical ensemble | p. 150 |
| A master equation view of Bose condensation | p. 152 |
| exact treatment of condensate traps | p. 155 |
| References | p. 158 |
| Scaling, renormalization and the Ising model | p. 159 |
| Introduction | p. 159 |
| Mean field theory and critical indices | p. 160 |
| Scaling | p. 167 |
| Renormalization | p. 169 |
| Renormalization and scaling | p. 172 |
| Two-dimensional Ising model renormalization | p. 174 |
| References | p. 177 |
| Relativistic covariant statistical mechanics of many particles | p. 178 |
| Introduction | p. 178 |
| Quantum many-particle dynamics: the event picture | p. 180 |
| Two-event Boltzmann equation | p. 183 |
| Some results of the quantum event Boltzmann equation | p. 187 |
| Relativistic quantum equilibrium event ensembles | p. 191 |
| References | p. 197 |
| Quantum optics and damping | p. 199 |
| Introduction | p. 199 |
| Atomic damping: atomic master equation | p. 199 |
| Cavity damping: the micromaser: detection | p. 206 |
| Detection master equation for the cavity field | p. 207 |
| the field Quantization and interaction | p. 214 |
| References | p. 219 |
| Entanglements | p. 221 |
| Introduction | p. 221 |
| Entanglements: foundations | p. 221 |
| Entanglements: Q bits | p. 224 |
| Entanglement consequences: quantum teleportation, the Bob and Alice story | p. 226 |
| Entanglement consequences: dense coding | p. 228 |
| Entanglement consequences: quantum computation | p. 228 |
| Decoherence: entanglement destruction | p. 231 |
| Decoherence correction (error correction) | p. 235 |
| entanglement and the Schmidt decomposition | p. 236 |
| References | p. 238 |
| Quantum measurement and irreversibility | p. 240 |
| Introduction | p. 240 |
| Ideal quantum measurement | p. 241 |
| Irreversibility: measurement master equations | p. 243 |
| An Open system master equation model for measurement | p. 246 |
| Stochastic energy based collapse | p. 248 |
| References | p. 251 |
| Quantum Langevin equation and quantum Brownian motion | p. 253 |
| Introduction | p. 253 |
| Quantum Langevin equation | p. 254 |
| Quantum Langevin equation with measurement | p. 260 |
| References | p. 262 |
| Linear response: fluctuation and dissipation theorems | p. 264 |
| Introduction | p. 264 |
| Quantum linear response in the steady state | p. 266 |
| Linear response, time dependent | p. 269 |
| Fluctuation and dissipative theorems | p. 272 |
| Comments and comparisons | p. 277 |
| References | p. 279 |
| Time-dependent quantum Green's functions | p. 281 |
| Introduction | p. 281 |
| One- and two-time quantum Green's functions and their properties | p. 282 |
| Analytic properties of Green's functions | p. 284 |
| Connection to linear response theory | p. 288 |
| Green's function hierarchy truncation | p. 289 |
| Keldysh time-loop path perturbation theory | p. 297 |
| References | p. 302 |
| Decay scattering | p. 303 |
| Basic notions and the Wigner-Weisskopf theory | p. 303 |
| Wigner-Weisskopf method: pole approximation | p. 306 |
| Wigner-Weisskopf method and Lee-Friedrichs model with a single channel | p. 312 |
| Wigner-Weisskopf and multichannel decay | p. 318 |
| Wigner-Weisskopf method with many-channel decay: the Lee-Friedrichs model | p. 321 |
| Gel'fand triple | p. 332 |
| Lax-Phillips theory | p. 335 |
| Application to the Stark model | p. 354 |
| References | p. 362 |
| Quantum statistical mechanics, extended | p. 365 |
| Intrinsic theory of irreversibility | p. 365 |
| Complex Liouvillian eigenvalue method: introduction | p. 366 |
| Operators and states with diagnoal singularity | p. 367 |
| Super operators and time evolution | p. 369 |
| Subdynamics and analytic continuation | p. 371 |
| The Pauli equation revisited | p. 375 |
| References | p. 378 |
| Quantum transport with tunneling and reservoir ballistic transport | p. 379 |
| Introduction | p. 379 |
| Pauli equation and boundary interaction | p. 380 |
| Ballistic transport | p. 383 |
| Green's function closed-time path theory to transport | p. 385 |
| References | p. 389 |
| Black hole thermodynamics | p. 390 |
| Introduction to black holes | p. 390 |
| Equilibrium Thermodynamic analogies: the first law | p. 394 |
| The second law of thermodynamics and black holes | p. 397 |
| Extended entropy principle for black holes | p. 399 |
| Acausal evolution: extended irreversible dynamics in black holes | p. 401 |
| Reference | p. 401 |
| A Problems | p. 404 |
| Comments on the problems | p. 404 |
| "Foundations" problems | p. 404 |
| Kinetic dynamics problems | p. 407 |
| Equilibrium and phase transition problems | p. 409 |
| References | p. 410 |
| Index | p. 411 |
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