Methods of Statistical Physics

Chapter 1 - Kinetic Equations for Classical Systems 1.1. Many-Particle Distribution Functions 1.1.1. Boltzmann's Kinetic Equation 1.1.2. Probability Density of Phase Points 1.1.3. Equations for Many - Particle Distribution Functions 1.2. Integral Equations for Many - Particle Distribution Functions 1.2.1. Integral Equations for Distribution Functions at the Kinetic Stage of Evolution 1.2.2. Construction of a Perturbation Theory for Systems with a Low Particle Density 1.3. Kinetic Equations and Transport Phenomena in Gases 1.3.1. Kinetic Equation in the Case of Weak Interactions 1.3.2. Kinetic Equation in the Low Density Case 1.3.3. Theory of Transport Phenomena in Gases 1.4. Kinetic Equations for Particles Interacting with a Medium 1.4.1. The Fokker-Planck Equation for Slow Processes 1.4.2. The Theory of Brownian Movement 1.4.3. The Theory of Neutron Moderation 1.5. Statistical Mechanics of a System of Charged Particles 1.5.1. A Kinetic Equation for Electrons in a Plasma 1.5.2. Theory of Screening 1.5.3. Dispersion Equation for Waves in Plasmas 1.6. Irreversibility of Macroscopic Processes and the Ergodic Hypothesis 1.6.1. Reversibility of Mechanical Motions and Irreversibility of Macroscopic Processes 1.6.2. The Ergodic HypothesisChapter 2 - General Principles of the Statistical Mechanics of Quantum Systems 2.1. Principles of Quantum Mechanics 2.1.1. Pure States and Mixed States 2.1.2. The Dynamic Law of Quantum Mechanics 2.1.3. The Measuring Process 2.2. Second Quantization 2.2.1. Particle Creation and Annihilation Operators 2.2.2. Operators of Physical Quantities 2.3. Symmetry of Equations of Quantum Mechanics 2.3.1. Invariance of Equations of Quantum Mechanics Relative to Continuous Transformations 2.3.2. Invariance of Equations of Quantum Mechanics under Spatial Reflection and Time Reversal 2.4. The Principle of Attenuation of Correlations and Ergodic Relations for Quantum Systems 2.4.1. The Principle of Attenuation of Correlations 2.4.2. Equations of Motion 2.4.3. Ergodic Relations for Quantum SystemsChapter 3 - Theory of Equilibrium States of Quantum Systems 3.1.Theory of Weakly Non-Ideal Quantum Gases 3.1.1. The Bose-Einstein and Fermi-Dirac Distributions 3.1.2. Thermodynamic Perturbation Theory 3.1.3. Quantum Virial Expansions 3.2. Superfluidity of a Gas of Bosons or Fermions 3.2.1. Quasi-Averages 3.2.2. Theory of Superfluidity of a Bose Gas 3.2.3. Theory of Superfluidity of a Fermi Gas and the Phenomenon of SuperconductivityChapter 4 - Methods of Investigating Non-Equilibrium States of Quantum Systems 4.1. The Reaction of a System to an External Perturbation 4.1.1. The Statistical Operator of a System Located in a Weak External Field 4.1.2. Properties of the Green Functions 4.2. General Theory of Relaxation Processes 4.2.1. An Integral Equation for the Statistical Operator in the Case of Weak Interactions 4.2.2. An Integral Equation for the Statistical Operator in the Case of Small Inhomogeneities 4.2.3. An Integral Equation for the Statistical Operator of In homogeneous Systems with Weak Interactions 4.3. Summation of Secular Terms 4.3.1. Asymptotic Operators 4.3.2. A Functional Equation for the Asymptotic Operators 4.3.3. Summation of Secular Terms and the Coarse-Grained Statistical Operators 4.4. The Low-Frequency Asymptotics of the Green Functions 4.4.1. Linearization of the Equations for the Course-Grained Statistical Operator 4.4.2.