This text provides an introduction to nonequilibrium statistical mechanics. It stresses fundamental concepts and the latest methods, rather than individual applications, and will be of interest to advanced students and re- searchers.

Klappentext

Statistical Physics II introduces nonequilibrium theories of statistical mechanics from the viewpoint of the fluctuation-disipation theorem. Emphasis is placed on the relaxation from nonequilibrium to equilibrium states, the response of a system to an external disturbance, and general problems involved in deriving a macroscopic physical process from more basic underlying processes. Fundamental concepts and methods are stressed, rather than the numerous individual applications.

Inhalt

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.- 3.1.1 Mechanical and Thermal Forces vs Displacements and Currents.- 3.1.2 Linear Relations.- 3.1.3 Response to a Pulsed Force.- 3.1.4 Relaxation Phenomena.- 3.2 Complex Admittance.- 3.2.1 Harmonic (Fourier) Analysis.- 3.2.2 Energy Dissipation.- 3.3 Debye Relaxation.- 3.3.1 Dielectric Relaxation.- 3.3.2 Response Functions with Exponential Damping.- 3.3.3 Solution of Polar Molecules.- 3.4 Resonance Absorption.- 3.4.1 Van Vleck-Weisskopf-Fröhlich Type Resonance Absorption.- 3.4.2 Nuclear Magnetic Resonance.- 3.4.3 Failure at High Frequencies.- 3.5 Wave Number-Dependent Complex Admittance.- 3.5.1 Non-Markovian Nonlocal Linear Relations.- 3.5.2 Complex Admittance for the Diffusion Phenomenon.- 3.6 Dispersion Relations.- 3.6.1 Proof of the Dispersion Relations.- 3.6.2 Dispersion Relations and Causality.- 3.6.3 Analytical Continuation into the Complex Plane.- 3.7 Sum Rules and Interpolation Formulas.- 3.7.1 Moment Sum Rules.- 3.7.2 Non-Markovian Law of Diffusion.- 4. Statistical Mechanics of Linear Response.- 4.1 Static Response to External Force.- 4.1.1 Static Admittance and the Canonical Correlation.- 4.2 Dynamic Response to External Force.- 4.2.1 The Response Function and the Poisson Bracket.- 4.2.2 Kubo Formula.- 4.2.3 Initial Values of the Response Function and Its Derivatives.- 4.3 Symmetry and the Dispersion Relations.- 4.3.1 Spectral Function and Its Symmetry.- 4.3.2 Symmetry in the Current Response.- 4.3.3 Symmetry in the Displacement Response.- 4.3.4 Proof of the Dispersion Relations.- 4.4 Fluctuation and Dissipation Theorem.- 4.4.1 Symmetrized Correlation.- 4.4.2 The Equivalence Between the Symmetrized Correlation Function and the Response or the Relaxation Function.- 4.4.3 Fluctuation-Dissipation Theorem.- 4.5 Density Response, Conduction and Diffusion.- 4.5.1 Density and Current in Response to the External Field.- 4.5.2 Relaxation of the Density Response and the Density Fluctuation.- 4.5.3 Shielding of the External Potential.- 4.5.4 Resistivity Formula.- 4.5.5 Dielectric Shielding and Electric Conductivity.- 4.5.6 Kramers-Kronig Relations and the Sum Rules.- 4.6 Response to Thermal Internal Forces.- 4.6.1 Onsager's Postulate.- 4.6.2 Fluctuation of Macrovariables as Brownian Motion.- 4.6.3 A General Formulation of Onsager's Postulate.- 4.6.4 Nonequilibrium Density Matrix.- 4.7 Some Remarks on the Linear-Response Theory.- 4.7.1 The Kinetic Method Versus the Linear-Response Theory.- 4.7.2 Van Kampen's Objection.- 4.7.3 Spurious Singularities at the Zero Value of the External Field.- 4.7.4 Singularities at k = 0, ? = 0.- 5. Quantum Field Theoretical Methods in Statistical Mechanics.- 5.1 Double-Time Green's Functions.- 5.1.1 Retarded Green's Functions.- 5.1.2 Advanced Green's Functions.- 5.2 Chain of Equations of Motion and the Decoupling Approximation.- 5.2.1 Chain of Equations of Motion.- 5.2.2 Complex Dielectric Function of a Plasma in a Decoupling Approximation.- 5.3 Relation to the Kinetic Equation.- 5.3.1 Klimontovich Operator.- 5.3.2 Self-Consistent Field Approximation.- 5.3.3 Plasma Oscillation.- 5.4 Single-Particle Green's Function and the Causal Green's Function.- 5.4.1 Single-Particle Green's Functions.- 5.4.2 Single-Particle Green's Functions for Free Particles.- 5.4.3 Causal Green's Functions.- 5.5 Basic Formula for Perturbational Expansion.- 5.5.1 Perturbational Expansion of the Equilibrium Density Matrix.- 5.5.2 Perturbational Expansion of the Thermodynamic Potential.- 5.6 Temperature Green's function.- 5.6.1 Temperature Green's Functions (Matsubara-Green's Functions).- 5.6.2 Fourier Analysis of the Temperature Green's function.- 5.6.3 Single-Particle Temperature Green's Function for Noninteracting Particles.- 5.6.4 Abrikosov-Gor'kov-Dzyaloshinskii-Fradkin Theorem.- 5.7 Diagram Technique.- 5.7.1 Bloch - De Dominicis Theorem.- 5.7.2 Perturbational Expansion of 0.- 5.7.3 Correspondence with Feynman Diagrams.- 5.7.4 Matsubara Formula.- 5.8 Dyson Equation.- 5.8.1 Single-Particle Temperature Green's function.- 5.8.2 Graphical Summation.- 5.8.3 Feynman Rules.- 5.9 Relationship Between the Thermodynamic Potential and the Temperature Green's Function.- 5.10 Special Case of the Two-Particle Green's function.- 5.10.1 Two-Particle Green's Function of Zeroth-Order for a Plasma.- 5.10.2 Polarization Operator.- 5.10.3 Electric Charge Density Green's function.- General Bibliography of Textbooks.- References.