Statistical Physics

Preface Acknowledgments Part I. Principles and Elementary Applications 1. Kinetic Theory 1.1. Boltzmann Equation 1.2. Maxwell-Boltzmann Distribution Function 1.3. Calculation of Averages 1.4. Spectral Broadening By the Doppler Effect 1.5. Mean Free Path 1.6. Elementary Treatment of Transport Phenomena 1.7. Boltzmann and Gibbs References 2. Principles of Statistical Mechanics 2.1. Phase Space and the Liouville Theorem 2.2.* Ergodic Theories 2.3. H-Theorem for Systems in Equilibrium 2.4. Meanings of the Constants in the Canonical Distribution Function 2.5. Coarse-Graining 2.6. Product Approximation for the Distribution Function 2.7. H-Theorem Based on the Master Equation 42 Problems References 3. Partition Functions 3.1. Boltzmann Statistics 3.2. Partition Function 3.3. Gibbs'S Paradox 3.4. Grand Ensemble 3.5. Relation Between the Canonical and Grand Canonical Partition Functions 3.6. Fluctuations 3.7. The Elasticity of Rubber 3.8. Lattice Defects Problems References 4. Ideal Bosons and Fermions 4.1. Blackbody Radiation 4.2. Specific Heats of Solids 4.3. Quantum Statistics of Ideal Gases 4.4. Bose-Einstein Condensation 4.5. Phonons and Rotons 4.6. Heat Capacities of Fermi Gases and Fermi Liquids 4.7. Elementary Treatment of Transport Phenomena in Degenerate Gases 4.8. De Haas-Van Alphen Effect 4.9.* Parastatistics Problems References Part II. Classical Interacting Systems 5. Linked Cluster Expansion 5.1. Second Virial Coefficient 5.2. Cluster Expansion 5.3. Virial Expansion 5.4. Irreducible Integrals 5.5. Cumulant Expansion 5.6. Ring Diagram Approximation for a Classical Electron Gas 5.7. Theory of Condensation 5.8. Polarizable Gases 5.9. Bounds of the Free Energy 5.10.* Cluster Expansions for Binary Mixtures Problems References 6. Distribution Functions 6.1. Reduced Liouville Equation and Boltzmann Equation 6.2. Stress Tensor in Nonequilibrium Fluids 6.3. Viscosity Coefficient of Fluids 6.4. Plasmas 6.5. Viri A1 Equation of State 6.6. Determination of Fluid Structure 6.7. Critical Opalescence 6.8. Expansions of Distribution Functions 6.9.* Nodal Expansion 6.10.* HNC and PY Approximations 6.11.* Born-Green Theory Problems References 7. Brownian Motion 7.1. Random Walks and Brownian Motion 7.2.* Random Walks on Lattices 7.3.* Stokes Friction and Einstein Viscosity 7.4. Langevin's Equation 7.5. Friction Coefficient of a Brownian Particle 7.6. Autocorrelation Function 7.7. Neutron Scattering 7.8. The Fokker-Planck Equation 7.9.* Self-Avoiding Walk Problem Problems References 8. Lattice Statistics 8.1. One-Dimensional Lattice 8.2.* Helix-Coil Transition in Polypeptide and "Melting" of DNA 8.3. Duality Principle 8.4.* Rigorous Theory of a Two-Dimensional Rectangular Lattice 8.5. Spin Correlation Functions 8.6. Lattice Gas 8.7. Distribution of Zeros of the Grand Partition Function 8.8. Frequency Spectrum 8.9.* Lattice Green's Function 8.10.* Spherical Model 8.11.* Heisenberg Model References 9. Phenomena Near the Critical Temperature 9.1. Critical Temperature of a Fluid 9.2. Relationships among the Critical Exponents 9.3. Magnetic Phase Transitions 9.4. Binary Mixtures 9.5. Quantum Liquid Solution 9.6. Order-Disorder Theory 9.7. Density Fluctuations near Critical Temperature 9.8. Spatial Correlation of a Bose Gas near the Condensation Temperature 9.9. Transport Coefficients near Critical Points References Part Iii. Quantum Interacting Systems 10. Propagator Methods for the Partition Functions 10.1. Density Matrix 10.2. Density Matrix in the Canonical Ensemble 10.3. Simple Examples of the Density Matrix 10.4. Propagator in the R-ß Space 10.5. Graphic Representation of Propagators 10.6. Linked Cluster Expansion of the Equation of State 10.7. Equation of State in the Ring Diagram Approximation 10.8.* The Eigenvalues of Quantum Propagators 10.9. Correlation Energy of an Electron Gas Problems References 11. Propagator Methods for Distribution Functions 11.1. Linked Cluster Expansions of Distribution Functions 11.2. Distribution Functions of Ideal Quantum Gases 11.3. Triplet Distribution Function 11.4. Chain Diagram Approximation 11.5. Classical Electron Gas 11.6.* Charged Fermions 11.7.* Charged Bosons 11.8.* Phonon Spectrum and Spatial Correlations in a Hard-Sphere Bose Gas 11.9.* Hard-Sphere Fermions Problems References 12. Transport Phenomena in Degenerate Systems 12.1. Uehling-Uhlenbeck Equation 12.2. Transport Coefficients 12.3. Transport Phenomena in Degenerate Systems 12.4. Phonon-Phonon Scattering 12.5. Electrical Conductivity of Metals 12.6.* Resistance Minima in Dilute Magnetic Alloys Problems References 13. Irreversibility and Transport Coefficients 13.1. Response to External Forces 13.2. Kramers-Kronig Relations for the Response Function 13.3. Symmetry Properties of Response Functions 13.4. Response in Canonical Ensembles 13.5. Transport Coefficients 13.6. Reduction of Transport Coefficients 13.7.* Cluster Expansion of Time Correlation Functions 13.8.* Master Equation Problems References 14. Second Quantization 14.1. Number Operator 14.2. Interaction Hamiltonian 14.3. Lattice Vibrations 14.4. Phonon Spectrum in a Degenerate Bose Gas 14.5. Electron Gas 14.6. Electron-Phonon Interaction 14.7. Electron-Electron Interaction Via Phonons 14.8. ⌠-Sum Rule 14.9. Dielectric Constant of a Plasma 14.10.* Spin and Statistics Problems References 15. Green'S Functions 15.1. Temperature Green's Function 15.2. Properties of the Green's Function 15.3. Contraction 15.4. Perturbation Calculation of the Grand Partition Function 15.5. Interaction Representation and Lehmann Representation 15.6. Applications of a One-Body Time Green's Function 15.7. Response Functions 15.8. Equations of Motion 15.9.* Superconductivity References Subject Index