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[资源] Elements Of Statistical Mechanics - With An Introduction To Quantum Field Theory

Contents
Preface page ix
List of fundamental physical constants xii
1 The problem 1
1.1 A molecular model 1
1.2 The basics of classical thermodynamics 2
1.3 The zeroth law of thermodynamics 6
1.4 The first law, heat 9
1.5 The second law, entropy 12
1.6 Gibbs phase rule 22
1.7 Thermodynamic potentials 23
1.8 The third law 29
2 Statistical mechanics 35
2.1 Fundamental ideas 35
2.2 The canonical ensemble 36
2.3 The perfect gas 38
2.4 The Gibbs paradox 40
2.5 Thermal properties of the classical perfect gas 42
2.6 Paramagnetic systems 43
2.7 The one-dimensional Ising model 45
2.8 Applications in biology 48
3 Variations of a theme 56
3.1 The grand canonical ensemble 56
3.2 Density fluctuations 60
3.3 Entropy and the Boltzmann constant 62
3.4 Micro canonical ensemble 62
3.5 The full picture 65
4 Handling interactions 70
4.1 Statement of the problem 70
v
vi Contents
4.2 Example: van der Waals equation of state 71
4.3 General theory: the cluster expansion 74
4.4 Relation to experiment: the virial expansion 79
5 Monte Carlo integration 82
5.1 Numerical integration techniques 82
5.2 Markov processes 86
5.3 The Ising model 95
5.4 Implementation of the algorithm 99
5.5 The Lennard-Jones fluid 102
6 Numerical molecular dynamics 112
6.1 Equations of motion and the micro canonical ensemble 112
6.2 Numerical integration 120
6.3 Choices of algorithm 122
6.4 The Lennard-Jones fluid 134
7 Quantum statistical mechanics 141
7.1 Quantum mechanics 141
7.2 The quantum partition function 145
7.3 Fermi–Dirac system 146
7.4 Bose–Einstein systems 156
7.5 Specific heat for a solid 163
7.6 Photons 165
7.7 Phonons 166
7.8 Density matrix 168
8 Astrophysics 175
8.1 Basic problem 175
8.2 White dwarf stars 180
8.3 Chemical reactions 183
8.4 Saha ionization formula 185
8.5 Neutron stars 187
8.6 Blackbody spectrum of the Universe 188
9 Non-relativistic quantum field theory 194
9.1 The quantum field theory formulation 194
9.2 Perturbation theory 206
9.3 Wick’s theorem 209
9.4 Green functions 212
9.5 Feynman rules 215
9.6 Scattering cross-section for two helium atoms 220
9.7 Fermions at finite density 224
9.8 Finite temperature perturbation theory 227
9.9 Relativistic effects 230
Contents vii
10 Superfluidity 235
10.1 Quantum field theory formulation 237
10.2 The quasi-particle approach 238
10.3 Green function approach 245
10.4 Summary 249
11 Path integrals 252
11.1 Quantum mechanics 252
11.2 Quantum field theory 261
11.3 Real time path integral 267
11.4 Relativistic scalar field 269
12 A second look 272
12.1 The connection – reversibility 273
12.2 Poincaré recurrence 274
12.3 Ergodicity 276
12.4 Equipartition law and temperature 278
12.5 Density of states and surface effects 285
12.6 Zero-point energy 287
12.7 Internal degrees of freedom 289
13 Phase transitions and the renormalization group 295
13.1 Basic problem 295
13.2 Peierls argument 299
13.3 Landau theory of phase transitions 301
13.4 Renormalization group 308
13.5 Critical exponent calculations 314
13.6 Correlation functions 317
13.7 Epsilon expansion 319
Index 331
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