Statistical Physics II

1. Brownian Motion.- 1.1 Brownian Motion as a Stochastic Process.- 1.2 The Central Limit Theorem and Brownian Motion.- 1.3 The Langevin Equation and Harmonic Analysis.- 1.4 Gaussian Processes.- 1.5 Brownian Motion Modeled by a Gaussian Process.- 1.6 The Fluctuation-Dissipation Theorem.- 2. Physical Processes as Stochastic Processes.- 2.1 Random Frequency Modulation.- 2.2 Brownian Motion Revisited.- 2.3 Markovian Processes.- 2.4 Fokker-Planck Equation.- 2.5 Contraction of Information. Projected Processes.- 2.6 Derivation of Master Equations.- 2.7 Brownian Motion of a Quantal System.- 2.8 Boltzmann Equation.- 2.9 Generalized Langevin Equation and the Damping Theory.- 3. Relaxation and Resonance Absorption.- 3.1 Linear Irreversible Processes.- 3.2 Complex Admittance.- 3.3 Debye Relaxation.- 3.4 Resonance Absorption.- 3.5 Wave Number-Dependent Complex Admittance.- 3.6 Dispersion Relations.- 3.7 Sum Rules and Interpolation Formulas.- 4. Statistical Mechanics of Linear Response.- 4.1 Static Response to External Force.- 4.2 Dynamic Response to External Force.- 4.3 Symmetry and the Dispersion Relations.- 4.4 Fluctuation and Dissipation Theorem.- 4.5 Density Response, Conduction and Diffusion.- 4.6 Response to Thermal Internal Forces.- 4.7 Some Remarks on the Linear-Response Theory.- 5. Quantum Field Theoretical Methods in Statistical Mechanics.- 5.1 Double-Time Green's Functions.- 5.2 Chain of Equations of Motion and the Decoupling Approximation.- 5.3 Relation to the Kinetic Equation.- 5.4 Single-Particle Green's Function and the Causal Green's Function.- 5.5 Basic Formula for Perturbational Expansion.- 5.6 Temperature Green's function.- 5.7 Diagram Technique.- 5.8 Dyson Equation.- 5.9 Relationship Between the Thermodynamic Potential and the Temperature Green'sFunction.- 5.10 Special Case of the Two-Particle Green's function.- General Bibliography of Textbooks.- References.