统计力学视频教程 复旦大学 101讲 陈焱主讲

 
课程名称：统计力学视频教程 复旦大学 101讲 陈焱主讲
 
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课程目录：
 
Cover image 
Title page 
Table of Contents 
Copyright 
Preface to the Third Edition 
Preface to the Second Edition 
Preface to the First Edition 
Historical Introduction 
Chapter 1: The Statistical Basis of Thermodynamics 
1.1 The macroscopic and the microscopic states 
1.2 Contact between statistics and thermodynamics: physical significance of the number Ω(N, V, E) 
1.3 Further contact between statistics and thermodynamics 
1.4 The classical ideal gas 
1.5 The entropy of mixing and the Gibbs paradox 
1.6 The “correct” enumeration of the microstates 
Problems 
Chapter 2: Elements of Ensemble Theory 
2.1 Phase space of a classical system 
2.2 Liouville’s theorem and its consequences 
2.3 The microcanonical ensemble 
2.4 Examples 
2.5 Quantum states and the phase space 
Problems 
Chapter 3: The Canonical Ensemble 
3.1 Equilibrium between a system and a heat reservoir 
3.2 A system in the canonical ensemble 
3.3 Physical significance of the various statistical quantities in the canonical ensemble 
3.4 Alternative expressions for the partition function 
3.5 The classical systems 
3.6 Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble 
3.7 Two theorems — the “equipartition” and the “virial” 
3.8 A system of harmonic oscillators 
3.9 The statistics of paramagnetism 
3.10 Thermodynamics of magnetic systems: negative temperatures 
Problems 
Chapter 4: The Grand Canonical Ensemble 
4.1 Equilibrium between a system and a particle-energy reservoir 
4.2 A system in the grand canonical ensemble 
4.3 Physical significance of the various statistical quantities 
4.4 Examples 
4.5 Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles 
4.6 Thermodynamic phase diagrams 
4.7 Phase equilibrium and the Clausius–Clapeyron equation 
Problems 
Chapter 5: Formulation of Quantum Statistics 
5.1 Quantum-mechanical ensemble theory: the density matrix 
5.2 Statistics of the various ensembles 
5.3 Examples 
5.4 Systems composed of indistinguishable particles 
5.5 The density matrix and the partition function of a system of free particles 
Problems 
Chapter 6: The Theory of Simple Gases 
6.1 An ideal gas in a quantum-mechanical microcanonical ensemble 
6.2 An ideal gas in other quantum-mechanical ensembles 
6.3 Statistics of the occupation numbers 
6.4 Kinetic considerations 
6.5 Gaseous systems composed of molecules with internal motion 
6.6 Chemical equilibrium 
Problems 
Chapter 7: Ideal Bose Systems 
7.1 Thermodynamic behavior of an ideal Bose gas 
7.2 Bose-Einstein condensation in ultracold atomic gases 
7.3 Thermodynamics of the blackbody radiation 
7.4 The field of sound waves 
7.5 Inertial density of the sound field 
7.6 Elementary excitations in liquid helium II 
Problems 
Chapter 8: Ideal Fermi Systems 
8.1 Thermodynamic behavior of an ideal Fermi gas 
8.2 Magnetic behavior of an ideal Fermi gas 
8.3 The electron gas in metals 
8.4 Ultracold atomic Fermi gases 
8.5 Statistical equilibrium of white dwarf stars 
8.6 Statistical model of the atom 
Problems 
Chapter 9: Thermodynamics of the Early Universe 
9.1 Observational evidence of the Big Bang 
9.2 Evolution of the temperature of the universe 
9.3 Relativistic electrons, positrons, and neutrinos 
9.4 Neutron fraction 
9.5 Annihilation of the positrons and electrons 
9.6 Neutrino temperature 
9.7 Primordial nucleosynthesis 
9.8 Recombination 
9.9 Epilogue 
Problems 
Chapter 10: Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions 
10.1 Cluster expansion for a classical gas 
10.2 Virial expansion of the equation of state 
10.3 Evaluation of the virial coefficients 
10.4 General remarks on cluster expansions 
10.5 Exact treatment of the second virial coefficient 
10.6 Cluster expansion for a quantum-mechanical system 
10.7 Correlations and scattering 
Problems 
Chapter 11: Statistical Mechanics of Interacting Systems: The Method of Quantized Fields 
11.1 The formalism of second quantization 
11.2 Low-temperature behavior of an imperfect Bose gas 
11.3 Low-lying states of an imperfect Bose gas 
11.4 Energy spectrum of a Bose liquid 
11.5 States with quantized circulation 
11.6 Quantized vortex rings and the breakdown of superfluidity 
11.7 Low-lying states of an imperfect Fermi gas 
11.8 Energy spectrum of a Fermi liquid: Landau’s phenomenological theory21 
11.9 Condensation in Fermi systems 
Problems 
Chapter 12: Phase Transitions: Criticality, Universality, and Scaling 
12.1 General remarks on the problem of condensation 
12.2 Condensation of a van der Waals gas 
12.3 A dynamical model of phase transitions 
12.4 The lattice gas and the binary alloy 
12.5 Ising model in the zeroth approximation 
12.6 Ising model in the first approximation 
12.7 The critical exponents 
12.8 Thermodynamic inequalities 
12.9 Landau’s phenomenological theory 
12.10 Scaling hypothesis for thermodynamic functions 
12.11 The role of correlations and fluctuations 
12.12 The critical exponents ν and η 
12.13 A final look at the mean field theory 
Problems 
Chapter 13: Phase Transitions: Exact (or Almost Exact) Results for Various Models 
13.1 One-dimensional fluid models 
13.2 The Ising model in one dimension 
13.3 The n-vector models in one dimension 
13.4 The Ising model in two dimensions 
13.5 The spherical model in arbitrary dimensions 
13.6 The ideal Bose gas in arbitrary dimensions 
13.7 Other models 
Problems 
Chapter 14: Phase Transitions: The Renormalization Group Approach 
14.1 The conceptual basis of scaling 
14.2 Some simple examples of renormalization 
14.3 The renormalization group: general formulation 
14.4 Applications of the renormalization group 
14.5 Finite-size scaling 
Problems 
Chapter 15: Fluctuations and Nonequilibrium Statistical Mechanics 
15.1 Equilibrium thermodynamic fluctuations 
15.2 The Einstein–Smoluchowski theory of the Brownian motion 
15.3 The Langevin theory of the Brownian motion 
15.4 Approach to equilibrium: the Fokker–Planck equation 
15.5 Spectral analysis of fluctuations: the Wiener–Khintchine theorem 
15.6 The fluctuation–dissipation theorem 
15.7 The Onsager relations 
Problems 
Chapter 16: Computer Simulations 
16.1 Introduction and statistics 
16.2 Monte Carlo simulations 
16.3 Molecular dynamics 
16.4 Particle simulations 
16.5 Computer simulation caveats 
Problems 
Appendices 
Bibliography 
Index