Statistical Physics

Cover......Page 1
Title......Page 4
Copyright......Page 5
Preface......Page 6
Contents......Page 8
1 Basic principles of statistics......Page 12
1.2 Distribution functions......Page 13
1.3 Statistical independence......Page 18
1.4 Liouville theorem......Page 20
1.5 Role of energy, microcanonical distribution......Page 24
1.6 Partial distribution functions......Page 28
1.7 Density matrix......Page 32
1.7.1 Pure ensemble......Page 33
1.7.2 Mixed ensemble......Page 35
1.8 Quantum Liouville equation......Page 37
1.9 Microcanonical distribution in quantum statistics......Page 39
1.10 Partial density matrices......Page 40
1.11.1 Gibbs entropy. Entropy and probability......Page 43
1.11.2 The law of entropy growth......Page 46
2.1 Canonical distribution......Page 54
2.2 Maxwell distribution......Page 59
2.3 Free energy from Gibbs distribution......Page 61
2.4 Gibbs distribution for systems with varying number of particles......Page 63
2.5 Thermodynamic relations from Gibbs distribution......Page 66
3.1 Boltzmann distribution......Page 71
3.2 Boltzmann distribution and classical statistics......Page 72
3.3 Nonequilibrium ideal gas......Page 74
3.4 Free energy of Boltzmann gas......Page 77
3.5 Equation of state of Boltzmann gas......Page 78
3.6 Ideal gas with constant specific heat......Page 80
3.7 Equipartition theorem......Page 81
3.8 One-atom ideal gas......Page 83
4.1 Fermi distribution......Page 86
4.2 Bose distribution......Page 87
4.3 Nonequilibrium Fermi and Bose gases......Page 88
4.4 General properties of Fermi and Bose gases......Page 90
4.5 Degenerate gas of electrons......Page 93
4.6 Relativistic degenerate electron gas......Page 96
4.7 Specific heat of a degenerate electron gas......Page 97
4.8 Magnetism of an electron gas in weak fields......Page 99
4.9 Magnetism of an electron gas in high fields......Page 103
4.10 Degenerate Bose gas......Page 105
4.11 Statistics of photons......Page 108
5.1 Solid state at low temperature......Page 112
5.2 Solid state at high temperature......Page 115
5.3 Debye theory......Page 116
5.4 Quantum Bose liquid......Page 120
5.5 Superfluidity......Page 124
5.6 Phonons in a Bose liquid......Page 128
5.7 Degenerate interacting Bose gas......Page 132
5.8 Fermi liquids......Page 135
5.9 Electron liquid in metals......Page 141
6.1 Cooper instability......Page 144
6.2 Energy spectrum of superconductors......Page 146
6.3 Thermodynamics of superconductors......Page 155
6.4 Coulomb repulsion......Page 159
6.5 Ginzburg-Landau theory......Page 162
7.1 Gaussian distribution......Page 171
7.2 Fluctuations in basic physical properties......Page 175
7.3 Fluctuations in ideal gases......Page 178
8.1 Mean-field theory of magnetism......Page 181
8.2 Quasi-averages......Page 188
8.3 Fluctuations in the order parameter......Page 191
8.4 Scaling......Page 197
9.1 Linear response to mechanical perturbation......Page 206
9.2 Electrical conductivity and magnetic susceptibility......Page 212
9.3 Dispersion relations......Page 215
10.1 Boltzmann equation......Page 219
10.2 H-theorem......Page 225
10.3 Quantum kinetic equations......Page 227
10.3.1 Electron-phonon interaction......Page 229
10.3.2 Electron-electron interaction......Page 233
11.1 Quasiparticles and Green\'s functions......Page 236
11.2 Feynman diagrams for many-particle systems......Page 244
11.3 Dyson equation......Page 248
11.4 Effective interaction and dielectric screening......Page 252
11.5 Green’s functions at finite temperatures......Page 255
A.1 Ergodicity......Page 259
A.2 Poincare recurrence theorem......Page 265
A.3 Instability of trajectories and mixing......Page 267
B.1 Relation between Gibbs distributions and the principle of maximal information entropy......Page 270
B.2 Purging Maxwell\'s “demon”......Page 274
C.1 Quasi-equilibrium statistical operators......Page 281
C.2 Nonequilibrium statistical operators and quasi-averages......Page 284
Bibliography......Page 288
Index......Page 290