Note: Intro -- Preface -- Reference -- Contents -- 1 Basic Physics of Gases and Plasmas -- 1.1 Matter in Form of Gases and Plasmas -- 1.2 Basic Physics of Gases -- 1.2.1 Classical Gas Laws -- 1.2.2 Third Law of Thermodynamics and the Roots of Quantum Statistics -- 1.3 Basic Physics of Plasmas -- 1.3.1 Coulomb Interactions and Ionization Equilibrium -- Ionization Equilibrium Between Atoms, Electrons and Ions -- 1.3.2 Different Plasma States on Earth -- References -- 2 Elements of Quantum Statistical Theory -- 2.1 Many-Body Quantum Theory -- 2.1.1 Quantum States -- 2.1.2 Identity and Symmetry -- Symmetry Postulate (Pauli's Postulate) -- Symmetry Principle (Pauli's-Principle) -- 2.2 Quantum Dynamics of Many Particles -- 2.2.1 Schrödinger Equation -- Dynamics of the Symmetry Properties (Blochinzew 1953) -- 2.2.2 Pure and Mixed Ensembles -- 2.3 Standard Approximations for Many-Particle States -- 2.3.1 Hartree-Fock Approximation -- 2.3.2 Born-Oppenheimer Approximation, Virial Theorem and Coulomb Stability -- 2.3.3 Thomas-Fermi Theory of Multi-Electron Atoms -- 2.4 Quantum Statistical Ensemble Theory -- 2.4.1 Microcanonical and Canonical Ensembles -- 2.4.2 Grand Canonical Ensembles -- 2.5 Theory of Fluctuations and Relaxation Processes -- 2.5.1 Einstein-Onsager Relaxation Theory -- Linear Relaxation Processes -- 2.5.2 Correlations, Spectra, and Symmetry Relations -- References -- 3 Ideal Quantum Gases -- 3.1 Quantum Statistics of Oscillator and Phonon Gases -- 3.1.1 Einstein Model of Oscillations in Crystals -- 3.1.2 Debye Theory of Phonon Excitations in Lattices -- 3.2 Statistics of Bose-Einstein and Fermi-Dirac Gases -- 3.2.1 Development of the Quantum Statistics of Gases -- 3.2.2 Gases as Particle Systems with Additive Hamiltonian -- 3.3 Fermi- and Bose Distributions -- 3.3.1 Bose-Einstein Gases -- 3.3.2 Fermi-Dirac Gases. , 3.4 Thermodynamics Properties of Bose-Einstein Gases -- 3.5 Black Body Radiation and Relativistic Gases -- 3.5.1 Planck's Law of Radiation -- 3.5.2 Radiation as a Relativistic Gas -- 3.6 Thermodynamic Functions of Fermi Gases -- 3.6.1 The Ideal Fermi Gas -- 3.6.2 Fermi Gases in the High- and Low-Temperature Limits -- 3.7 Density-Dependent Fermi Gas Functions -- 3.7.1 Expansions for Weakly Degenerated Fermi Gases -- 3.7.2 Thermodynamics in Full Density Range -- 3.8 Hartree-Fock Theory of Weakly Interacting Electron Gases -- References -- 4 Density Operators and Other Tools of Quantum Statistics -- 4.1 Density Matrices and Operators -- 4.1.1 Density Matrices -- 4.1.2 von Neumann's Density Operators and Time Evolution -- 4.1.3 Maximum Entropy Principle and Thermodynamic Functions -- 4.2 Representations in Coordinate Space and Two-Time Functions -- 4.2.1 Coordinate Representations and Bloch Equations -- 4.2.2 Two-Time Density Operators -- 4.3 Bogolyubov's Reduced Density Operators -- 4.4 Slater-, Wigner- and Klimontovich Representations -- 4.4.1 Slater Representations -- 4.4.2 Wigner-Representation -- 4.4.3 Klimontovich's Microscopic Density -- 4.5 Density Functionals, Virial Theorems and Stability -- 4.5.1 Kohn-Sham and Thomas-Fermi Functionals -- 4.5.2 Coulomb Stability and Virial Theorem -- 4.6 Second Quantization -- 4.6.1 Occupation Number Representations -- 4.6.2 Second Quantization -- 4.6.3 Klimontovich Operator in Second Quantization -- 4.7 Green's Functions -- 4.7.1 Definition and Relations for Green's Functions -- 4.7.2 Thermodynamics and Green's Functions -- 4.8 Pair Bound States and Bethe-Salpeter Equation -- References -- 5 Real Gas Quantum Statistics -- 5.1 Cluster Expansions for Real Gases -- 5.2 Slater Functions and Virial Coefficients -- 5.2.1 General Density Expansions -- 5.2.2 Slater Sums for Pair Correlations. , 5.3 The Second Virial Coefficient -- 5.3.1 Virial Coefficient Including Exchange Effects -- 5.3.2 Beth-Uhlenbeck Method for Non-associating Gases -- 5.4 Equation of State for Gases with Deep Bound States -- 5.4.1 Fugacity Expansions -- 5.4.2 Chemical Picture -- 5.5 Helium and Other Quantum Gases at Low Temperature -- 5.5.1 Virial Expansion for Helium -- 5.5.2 Phase Transitions in Low-Temperature Gases -- 5.6 Weakly Interacting Quantum Gases -- 5.6.1 Bloch Equation -- 5.6.2 Slater Function and Free Energy -- References -- 6 Quantum Statistics of Dilute Plasmas -- 6.1 Basic Physics of Plasmas -- 6.1.1 Screening and Lattice Formation in Coulomb Systems -- 6.1.2 The Divergence of the Partition Function -- 6.2 Pair Correlations on Non-degenerate Plasmas -- 6.2.1 Density Matrix of Pairs -- 6.2.2 Method of Effective Potentials -- 6.3 Thermodynamics of the Classical Electron Gas and Quantum Corrections -- 6.3.1 Classical Bogolyubov Expansions -- 6.3.2 Quantum Corrections -- 6.4 Screening and Thermodynamic Functions of Non-degenerate Plasmas -- 6.4.1 Debye-Hückel Screening -- 6.4.2 Ring Functions -- 6.5 The Pair Bound State Contributions -- 6.5.1 Mean-Mass Approximation-Symmetrical Plasmas -- 6.5.2 The Second Virial Coefficient for General Plasmas -- 6.6 Evaluation of the Second Virial Coefficients -- 6.6.1 The Exchange Contributions to the Virial Functions -- 6.6.2 Direct Contributions to the Virial Functions -- References -- 7 Non-ideality and Deep Bound States in Plasmas -- 7.1 Higher Order Expansions with Respect to Density -- 7.1.1 Cluster Expansions with Respect to Density -- 7.1.2 Density Expansions of Pressure and Free Energy -- 7.2 Bound States and Fugacity Expansions -- 7.2.1 Cluster Series in Fugacity -- 7.2.2 Series in Powers of Fugacity -- 7.3 Bound States and Saha Equation -- 7.3.1 Fugacity Expansion and Ideal Mass Action Laws. , 7.3.2 Ionization and Saha Equation Including Screening -- 7.4 Further Problems of Non-ideality in Plasmas -- References -- 8 Non-equilibrium: Kinetic Equations -- 8.1 Development of Classical and Quantum Kinetic Theory -- 8.2 Pauli's Master Equation Approach and H-Theorem -- 8.3 Stochastic Dynamics Including a Heat Bath -- 8.4 Bogolyubov's Kinetic Theory Based on Reduced Density Operators -- 8.5 Bogolyubov's Derivation of the Quantum Boltzmann Equation -- 8.5.1 Operator Equations -- 8.5.2 Quantum Boltzmann Equation for Homogeneous Systems -- 8.6 Theory of Fluctuations and Fluctuation-Dissipation Relations -- 8.6.1 Basic Einstein-Onsager-Kubo Relations -- 8.6.2 Brownian Motion and Onsager-Casimir Relations -- 8.7 Quantum Fluctuation-Dissipation Relations -- 8.7.1 Nyquist Theorem and Callen-Welton Theorems -- 8.7.2 Klimontovich-Silin Theory of Plasma Fluctuations -- References -- Index.

Note: Intro -- Preface -- Contents -- 1 Physics of Dense Gases, Nonideal Plasmas, and High Energy Density Matter -- 1.1 Strongly Coupled Fluid Matter: A New Field of Physics -- 1.2 Physics of Dense Classical Fluids -- 1.2.1 Van der Waals Equation of State and Interactions -- 1.2.2 Statistical Theory of Dense Classical Gases -- 1.3 Quantum Physics of Strongly Coupled Gases -- 1.3.1 Correlations in Bose--Einstein and Fermi--Dirac Gases -- 1.3.2 Quantum Statistics of Interacting Gases -- 1.4 Ionic Fluids and Dense Low-Temperature Plasmas -- 1.4.1 Coulomb Forces and Debye--Hückel--Wigner Theories -- 1.4.2 Ionization and Association Equilibria -- 1.5 Quantum Statistics of Coulomb Systems -- 1.5.1 Quantum Interactions, Screening, and Regularization -- 1.5.2 Coulomb Phase Transitions -- 1.6 Development of Computer Simulation Methods -- 1.6.1 The Metropolis Algorithm -- 1.6.2 Monte Carlo and Molecular Dynamics Simulations -- 1.7 Transport Theory of Nonideal Gases and Plasmas -- 1.7.1 Extension of Boltzmann's Theory to Dense Gases -- 1.7.2 Kinetic Theory of Dense Plasmas -- 1.8 Dense Gases and Plasmas in the Laboratory and in the Sun -- 1.8.1 Studies of Ionization Phenomena -- 1.8.2 Generation of Fluids with High Energy Densities -- 1.9 Relativistic Plasmas and Matter with Extreme Energy Density -- 1.9.1 Relativistic, Subhadronic and Quark--Gluon Plasmas -- 1.9.2 Plasmas Generated by Relativistic Particle Beams -- 1.10 Dense Gases and Plasmas in Astrophysics -- 1.10.1 High Energy Densities in Astrophysical Systems -- 1.10.2 Relativistic Plasmas in Our Universe -- References -- 2 Strong Correlations and Equation of State of Dense Gases -- 2.1 Classical Molecular Distribution Functions and Density Expansions -- 2.1.1 Distribution Functions and Ornstein--Zernike Relations -- 2.1.2 Virial Expansions. , 2.2 Integral Equation Methods and Prototype Hard Sphere Systems -- 2.2.1 Percus--Yevick and Hypernetted-Chain Equations -- 2.2.2 Hard Core Fluids and Fluid Mixtures -- 2.3 Quantum Effects -- 2.3.1 Bose--Einstein and Fermi--Dirac Gases -- 2.3.2 Density Expansions Including Interaction Effects -- 2.4 Pair Correlations and Beth--Uhlenbeck Method -- 2.4.1 Slater Sums for Pairs and Second Virial Coefficient -- 2.4.2 Beth--Uhlenbeck Representation for Real Gases -- 2.5 Representations in the Grand Canonical Ensemble -- 2.5.1 Fugacity Expansions -- 2.5.2 Fugacity Expansions and the Chemical Picture -- 2.6 Strong Exchange Correlations in Fermi--Dirac Gases -- 2.6.1 Pair Correlations and Thermodynamics -- 2.6.2 Hartree--Fock Contributions -- 2.7 Quantum Statistics of Prototype Yukawa Gases -- 2.7.1 Perturbation Theory for Pair Density Operators -- 2.7.2 Perturbation Expansion for the Free Energy -- 2.8 Analytical Properties of Thermodynamic Functions of Yukawa Systems -- 2.8.1 Bound States and Analytical Properties -- 2.8.2 Exact Virial Coefficient and Thermodynamic Functions -- 2.9 Strongly Correlated Bose Gases at Low Temperatures -- 2.9.1 Noninteracting Bose Gases -- 2.9.2 Interacting Bose Gases and Phase Transitions -- References -- 3 Coulomb Systems. Screening and Ionization Problems -- 3.1 Classical Systems with Coulomb Interactions -- 3.1.1 Long Range of Coulomb Interactions. Screening -- 3.1.2 Plasma Parameter Expansions and Prototype Models -- 3.1.3 OCPs and the Ion Sphere Model -- 3.2 Charged Hard Sphere Systems -- 3.2.1 Debye--Hückel Approximation -- 3.2.2 Mean Spherical and Hypernetted Chain Approximations -- 3.3 Quantum Debye--Hückel Theory of Screening -- 3.3.1 Quantum Debye--Hückel Approximation -- 3.3.2 Reduced Mass Approximation -- 3.4 Slater Functions and Effective Potential Approach. , 3.4.1 Effective Potential Approach of Kelbg and Deutsch -- 3.4.2 Extensions by Wigner--Onsager Corrections -- 3.5 Plasmons and Collective Mode Expansions -- 3.5.1 Plasma Wave Excitations -- 3.5.2 Collective Mode Expansions -- 3.6 Ionization Equilibrium Between Atoms, Electrons, and Ions -- 3.6.1 Eggert--Saha Equation for Ideal Plasmas -- 3.6.2 Regularization of the Atomic Partition Function -- 3.7 Bound States and Ionization Equilibrium in Nonideal Plasmas -- 3.7.1 Weakly Nonideal EOS and Saha Equation -- 3.7.2 Nonideality in Atomic Partition Functions -- 3.8 Correlations in Noble Gas and Alkali Plasmas -- 3.8.1 Effective Potentials for Noble Gas and Alkali Plasmas -- 3.8.2 Correlations and Thermodynamic Functions -- 3.9 Models of First Order Phase Transitions in Ionized Gases -- 3.9.1 Van der Waals and Debye--Hückel--Bjerrum Models -- 3.9.2 Estimate of Critical Points in QDHA and KEPA -- 3.10 Discussion of Plasma Transitions in Theory and Experiment -- 3.10.1 Survey of Results on Plasmas and Ionic Fluids -- 3.10.2 PPT in Hydrogen, Noble Gas, and Alkali Plasmas -- References -- 4 Coulomb Correlations and EOS of Nondegenerate Nonideal Plasmas -- 4.1 Short-Range Quantum Effects in Low Density Plasmas -- 4.1.1 Pairs of Particles -- 4.1.2 Kelbg Potential -- 4.2 Screening in Weakly Coupled Plasmas -- 4.2.1 Screened Correlations in Nondegenerate Plasmas -- 4.2.2 Pair Correlations in Many-Component Systems -- 4.3 Non-diagonal Pair Density Operators -- 4.3.1 Diagonal and Non-diagonal Pair Density Matrix -- 4.3.2 Discussion of the Off-Diagonal Effective Potentials -- 4.4 Quantum Corrections in Thermodynamics -- 4.4.1 First Order Corrections to Classical OCP Results -- 4.4.2 Higher Order Screening Contributions -- 4.4.3 Screening in Weakly Correlated Mixtures -- 4.5 Virial Expansion in the Reduced Mass Approximation. , 4.5.1 Free Energy and Pressure in the RMA -- 4.5.2 Compatibility with the Mass Action Law Approach -- 4.6 Low Density Expansions for Coulomb Systems -- 4.6.1 Virial Expansion for Arbitrary Mass Relations -- 4.6.2 Screened Cluster Integrals -- 4.7 Exact Second Order Coulomb Virial Functions -- 4.7.1 Exchange Contribution to Coulomb Virial Functions -- 4.7.2 Direct Contributions to Coulomb Virial Functions -- 4.8 Discussion of Virial Functions and Thermodynamic Potentials -- 4.8.1 Analytical Properties of Virial Functions -- 4.8.2 Virial Expansion of Thermodynamic Functions -- References -- 5 Plasma Bound States in Grand Canonical and Mixed Representations -- 5.1 Fugacity Expansions of Thermodynamic Functions -- 5.1.1 Cluster Expansions in Fugacities -- 5.1.2 Fugacity Representations and the Saha Equation -- 5.2 Combinations Between Canonical and Grand-Canonical Density Expansions -- 5.2.1 Structure of the Lower Order Terms in the Density Expansion -- 5.2.2 Structure of Higher Order Contributions -- 5.3 Combined Density--Fugacity Expansions -- 5.3.1 Partial Summation of Density Series -- 5.3.2 Extended Representations of the EOS by Nonlinear Density Functions -- 5.4 Nonideality Effects in the Energy Spectrum -- 5.4.1 Energy Shifts in Effective Wave Equations -- 5.4.2 Hartree--Fock--Wigner Pressure at High Density -- References -- 6 Equations of State for Strongly Coupled Partially Ionized Plasmas -- 6.1 Coulomb Fluid Models and Electrical Field Energy -- 6.1.1 Electrical Field Correlations and Coulomb Energy -- 6.1.2 Coulomb Energy of Dense Electron Fluids -- 6.2 Chemical Potential and Internal Energy of Dense Electron--Ion Fluids -- 6.2.1 Reduced Mass Approximation and Beyond -- 6.2.2 Wigner Lattice Effects for Strong Coupling by Mode Restriction -- 6.2.3 Internal Energy of Free Charges Using HNC Calculations -- 6.3 Free Energy of Dense Plasmas. , 6.3.1 Main Contributions and Limits of the Free Energy -- 6.3.2 Padé Approximations for the Plasma Free Energy -- 6.4 Advanced Chemical Models Including Bound States -- 6.4.1 Free Energy in the Chemical Picture -- 6.4.2 Geometry of the Free Energy Landscape -- 6.5 Thermodynamics of High-Pressure Plasmas -- 6.5.1 Advanced Chemical Models with Energy Shifts -- 6.5.2 Methods for Minimizing the Free Energy -- 6.6 Hydrogen-Like and Helium-Like Plasmas at Ultrahigh Pressures -- 6.6.1 Hydrogen and Deuterium Hugoniots and Isentropes -- 6.6.2 Helium and Other Plasmas of Light Elements -- References -- 7 Kinetic Equations and Fluctuations in Nonideal Gases and Plasmas -- 7.1 Stochastic Kinetics -- 7.1.1 Smoluchowski--Fokker--Planck and Master Equations -- 7.1.2 Stochastic Kinetics of Pauli and Tolman -- 7.2 Quantum Kinetics and Transport Theory -- 7.2.1 Lorentz Kinetics and Relaxation Approximation -- 7.2.2 Bogoliubov Quantum Kinetic Theory -- 7.3 Irreversibility, Boltzmann, and Kullback Entropy. H-Theorems -- 7.3.1 Entropies and Pauli Dynamics -- 7.3.2 H-Theorems -- 7.4 Fluctuation--Dissipation Relations -- 7.4.1 Classical Relations -- 7.4.2 Quantum Fluctuation--Dissipation Relations -- 7.5 Plasma Fluctuations and Kinetic Equations -- 7.5.1 Quantum Correlations of the Electrical Field -- 7.5.2 Kinetic Equations and Fluctuation--Dissipation Relations -- References -- 8 Hopping Kinetics, Quantum Dynamics and Transport -- 8.1 Electron Hopping Kinetics -- 8.1.1 Hopping Dynamics of Electrons in Tight-Binding Models -- 8.1.2 Pauli Hopping Dynamics of Tight-Binding Electrons -- 8.2 Time Correlations and Linear Response -- 8.2.1 Time Correlations in the Tight-Binding Approximation -- 8.2.2 Linear Response Theory -- 8.3 Molecular Dynamics with Effective Potentials -- 8.3.1 Simple Models of Effective Interactions -- 8.3.2 Molecular Dynamics with Kelbg-Type Potentials. , 8.4 Wigner Dynamics with Momentum-Dependent Potentials.