Statistical Physics (eBook)

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Michael V. Sadovskii, Institute for Electrophysics, Russian Academy of Sciences, Russia.

Preface 5
1 Basic principles of statistics 11
1.1 Introduction 12
1.2 Distribution functions 12
1.3 Statistical independence 17
1.4 Liouville theorem 19
1.5 Role of energy, microcanonical distribution 23
1.6 Partial distribution functions 27
1.7 Density matrix 31
1.7.1 Pure ensemble 32
1.7.2 Mixed ensemble 34
1.8 Quantum Liouville equation 36
1.9 Microcanonical distribution in quantum statistics 38
1.10 Partial density matrices 39
1.11 Entropy 42
1.11.1 Gibbs entropy. Entropy and probability 42
1.11.2 The law of entropy growth 45
2 Gibbs distribution 53
2.1 Canonical distribution 53
2.2 Maxwell distribution 58
2.3 Free energy from Gibbs distribution 60
2.4 Gibbs distribution for systems with varying number of particles 62
2.5 Thermodynamic relations from Gibbs distribution 65
3 Classical ideal gas 70
3.1 Boltzmann distribution 70
3.2 Boltzmann distribution and classical statistics 71
3.3 Nonequilibrium ideal gas 73
3.4 Free energy of Boltzmann gas 76
3.5 Equation of state of Boltzmann gas 77
3.6 Ideal gas with constant specific heat 79
3.7 Equipartition theorem 80
3.8 One-atom ideal gas 82
4 Quantum ideal gases 85
4.1 Fermi distribution 85
4.2 Bose distribution 86
4.3 Nonequilibrium Fermi and Bose gases 87
4.4 General properties of Fermi and Bose gases 89
4.5 Degenerate gas of electrons 92
4.6 Relativistic degenerate electron gas 95
4.7 Specific heat of a degenerate electron gas 96
4.8 Magnetism of an electron gas in weak fields 98
4.9 Magnetism of an electron gas in high fields 102
4.10 Degenerate Bose gas 104
4.11 Statistics of photons 107
5 Condensed matter 111
5.1 Solid state at low temperature 111
5.2 Solid state at high temperature 114
5.3 Debye theory 115
5.4 Quantum Bose liquid 119
5.5 Superfluidity 123
5.6 Phonons in a Bose liquid 127
5.7 Degenerate interacting Bose gas 131
5.8 Fermi liquids 134
5.9 Electron liquid in metals 140
6 Superconductivity 143
6.1 Cooper instability 143
6.2 Energy spectrum of superconductors 145
6.3 Thermodynamics of superconductors 154
6.4 Coulomb repulsion 158
6.5 Ginzburg-Landau theory 161
7 Fluctuations 170
7.1 Gaussian distribution 170
7.2 Fluctuations in basic physical properties 174
7.3 Fluctuations in ideal gases 177
8 Phase transitions and critical phenomena 180
8.1 Mean-field theory of magnetism 180
8.2 Quasi-averages 187
8.3 Fluctuations in the order parameter 190
8.4 Scaling 196
9 Linear response 205
9.1 Linear response to mechanical perturbation 205
9.2 Electrical conductivity and magnetic susceptibility 211
9.3 Dispersion relations 214
10 Kinetic equations 218
10.1 Boltzmann equation 218
10.2 H-theorem 224
10.3 Quantum kinetic equations 226
10.3.1 Electron-phonon interaction 228
10.3.2 Electron-electron interaction 232
11 Basics of the modern theory of many-particle systems 235
11.1 Quasiparticles and Green's functions 235
11.2 Feynman diagrams for many-particle systems 243
11.3 Dyson equation 247
11.4 Effective interaction and dielectric screening 251
11.5 Green’s functions at finite temperatures 254
A Motion in phase space, ergodicity and mixing 258
A.1 Ergodicity 258
A.2 Poincare recurrence theorem 264
A.3 Instability of trajectories and mixing 266
B Statistical mechanics and information theory 269
B.1 Relation between Gibbs distributions and the principle of maximal information entropy 269
B.2 Purging Maxwell's “demon” 273
C Nonequilibrium statistical operators 280
C.1 Quasi-equilibrium statistical operators 280
C.2 Nonequilibrium statistical operators and quasi-averages 283
Bibliography 287
Index 289

lt;P>"The author of this book is devoted to the classical approach in statistical physics (usually related to equilibrium physics) – the presentation is given in such a way that reader with basic knowledge about this field can understand many of the presented aspects. […] This book is worth to be recommended." Zentralblatt für Mathematik