Nonequilibrium Statistical Physics -- Contents -- Preface -- 1 Introduction -- 1.1 Irreversibility: The Arrow of Time -- 1.1.1 Dynamical Systems -- 1.1.2 Thermodynamics -- 1.1.3 Ensembles and Probability Distribution -- 1.1.4 Entropy in Equilibrium Systems -- 1.1.5 Fundamental Time Arrows, Units -- 1.1.6 Example: Ideal Quantum Gases -- 1.2 Thermodynamics of Irreversible Processes -- 1.2.1 Quasiequilibrium -- 1.2.2 Statistical Thermodynamics with Relevant Observables -- 1.2.3 Phenomenological Description of Irreversible Processes -- 1.2.4 Example: Reaction Rates -- 1.2.5 Principle of Weakening of Initial Correlations and the Method of Nonequilibrium Statistical Operator -- Exercises -- 2 Stochastic Processes -- 2.1 Stochastic Processes with Discrete Event Times -- 2.1.1 Potentiality and Options, Chance and Probabilities -- 2.1.2 Stochastic Processes -- 2.1.3 Reduced Probabilities -- 2.1.4 Properties of Probability Distributions: Examples -- 2.1.5 Example: One-Step Process on a Discrete Space-Time Lattice and Random Walk -- 2.2 Birth-and-Death Processes and Master Equation -- 2.2.1 Continuous Time Limit and Master Equation -- 2.2.2 Example: Radioactive Decay -- 2.2.3 Spectral Density and Autocorrelation Functions -- 2.2.4 Example: Continuum Limit of Random Walk and Wiener Process -- 2.2.5 Further Examples for Stochastic One-Step Processes -- 2.2.6 Advanced Example: Telegraph Equation and Poisson Process -- 2.3 Brownian Motion and Langevin Equation -- 2.3.1 Langevin Equation -- 2.3.2 Solution of the Langevin Equation by Fourier Transformation -- 2.3.3 Example Calculations for a Langevin Process on Discrete Time -- 2.3.4 Fokker-Planck Equation -- 2.3.5 Application to Brownian Motion -- 2.3.6 Important Continuous Markov Processes -- 2.3.7 Stochastic Differential Equations and White Noise -- 2.3.8 Applications of Continuous Stochastic Processes.

Exercises -- 3 Quantum Master Equation -- 3.1 Derivation of the Quantum Master Equation -- 3.1.1 Open Systems Interacting with a Bath -- 3.1.2 Derivation of the Quantum Master Equation -- 3.1.3 Born-Markov and Rotating Wave Approximations -- 3.1.4 Example: Harmonic Oscillator in a Bath -- 3.1.5 Example: Atom Coupled to the Electromagnetic Field -- 3.2 Properties of the Quantum Master Equation and Examples -- 3.2.1 Pauli Equation -- 3.2.2 Properties of the Pauli Equation, Examples -- 3.2.3 Discussion of the Pauli Equation -- 3.2.4 Example: Linear Coupling to the Bath -- 3.2.5 Quantum Fokker-Planck Equation -- 3.2.6 Quantum Brownian Motion and the Classical Limit -- Exercises -- 4 Kinetic Theory -- 4.1 The Boltzmann Equation -- 4.1.1 Distribution Function -- 4.1.2 Classical Reduced Distribution Functions -- 4.1.3 Quantum Statistical Reduced Distribution Functions -- 4.1.4 The Stoßzahlansatz -- 4.1.5 Derivation of the Boltzmann Equation from the Nonequilibrium Statistical Operator -- 4.1.6 Properties of the Boltzmann Equation -- 4.1.7 Example: Hard Spheres -- 4.1.8 Beyond the Boltzmann Kinetic Equation -- 4.2 Solutions of the Boltzmann Equation -- 4.2.1 The Linearized Boltzmann Equation -- 4.2.2 Relaxation Time Method -- 4.2.3 The Kohler Variational Principle -- 4.2.4 Example: Thermal Conductivity in Gases -- 4.3 The Vlasov-Landau Equation and Hydrodynamic Equations -- 4.3.1 Derivation of the Vlasov Equation -- 4.3.2 The Landau Collision Term -- 4.3.3 Example for the Vlasov Equation: The RPA Dielectric Function -- 4.3.4 Equations of Hydrodynamics -- 4.3.5 General Remarks to Kinetic Equations -- Exercises -- 5 Linear Response Theory -- 5.1 Linear Response Theory and Generalized Fluctuation-Dissipation Theorem (FDT) -- 5.1.1 External Fields and Relevant Statistical Operator -- 5.1.2 Nonequilibrium Statistical Operator for Linear Response Theory.

5.1.3 Response Equations and Elimination of Lagrange Multipliers -- 5.1.4 Example: Ziman Formula for the Conductivity and Force-Force Correlation Function -- 5.1.5 The Choice of Relevant Observables and the Kubo Formula -- 5.2 Generalized Linear Response Approaches -- 5.2.1 Thermal Perturbations -- 5.2.2 Example: Thermoelectric Effects in Plasmas -- 5.2.3 Example: Hopping Conductivity of Localized Electrons -- 5.2.4 Time-Dependent Perturbations -- 5.2.5 Generalized Linear Boltzmann Equation -- 5.2.6 Variational Approach to Transport Coefficients -- 5.2.7 Further Results of Linear Response Theory -- Exercises -- 6 Quantum Statistical Methods -- 6.1 Perturbation Theory for Many-Particle Systems -- 6.1.1 Equilibrium Statistics of Quantum Gases -- 6.1.2 Three Relations for Elementary Perturbation Expansions -- 6.1.3 Example: Equilibrium Correlation Functions in Hartree-Fock Approximation -- 6.2 Thermodynamic Green's Functions -- 6.2.1 Thermodynamic Green's Functions: Definitions and Properties -- 6.2.2 Green's Function and Spectral Function -- 6.2.3 Example: Thermodynamic Green's Function for the Ideal Fermi Gas -- 6.2.4 Perturbation Theory for Thermodynamic Green's Functions -- 6.2.5 Application of the Diagram Rules: Hartree-Fock Approximation -- 6.3 Partial Summation and Many-Particle Phenomena -- 6.3.1 Mean-Field Approximation and Quasiparticle Concept -- 6.3.2 Dyson Equation and Self-Energy -- 6.3.3 Screening Equation and Polarization Function -- 6.3.4 Lowest Order Approximation for the Polarization Function: RPA -- 6.3.5 Bound States -- 6.3.6 Excursus: Solution to the Two-Particle Schr€odinger Equation with a Separable Potential -- 6.3.7 Cluster Decomposition and the Chemical Picture -- 6.4 Path Integrals -- 6.4.1 The Onsager-Machlup Function -- 6.4.2 Dirac Equation in 1 + 1 Dimensions -- Exercises.

7 Outlook: Nonequilibrium Evolution and Stochastic Processes -- 7.1 Stochastic Models for Quantum Evolution -- 7.1.1 Measuring Process and Localization -- 7.1.2 The Caldeira-Leggett Model and Quantum Brownian Motion -- 7.1.3 Dynamical Reduction Models -- 7.1.4 Stochastic Quantum Electrodynamics -- 7.1.5 Quantum Dynamics and Quantum Evolution -- 7.2 Examples -- 7.2.1 Scattering Theory -- 7.2.2 Bremsstrahlung Emission -- 7.2.3 Radiation Damping -- 7.2.4 The 1/f (Flicker) Noise -- 7.2.5 The Hydrogen Atom in the Radiation Field -- 7.2.6 Comments on Nonequilibrium Statistical Physics -- References -- Index.