Quantum Statistics of Charged Particle Systems

The year 1985 represents a special anniversary for people dealing with Ooulomb systems. 200 years ago, in 1785, Oharles Auguste de Ooulomb (1736-1806) found "Ooulomb's law" for the interaction force between charged particles. The authors want to dedicate this book to the honour of the great pioneer of electrophysics. Recent statistical mechanics is mainly restricted to systems of neutral particles. Except for a few monographs and survey articles (see, e. g., IOHIMARU, 1973, 1982; KUDRIN, 1974; KLIMONTOVIOH, 1975; EBELING, KRAEFT and KREMP, 1976, 1979; KALMAN and CARINI, 1978; BAUS and HANSEN, 1980; GILL, 1981, VELO and WIGHT­ MAN, 1981; MATSUBARA, 1982) the extended material on charged particle systems, which is now available thanks to the efforts of many workers in statistical mechanics, is widely dispersed in many original articles. It is the aim of this monograph to represent at least some part of the known results on charged particle systems from a unified point of view. Here the method of Green's functions turns out to be a powerful method especially to overcome the difficulties connected with the statistical physics of charged particle systems; some of them are . mentioned in the introduction. Here we can point, e.g., to the appearance of bound states in a medium and their role as new entities.

1. Introduction.- 2. Physical Concepts and Exact Results.- 2.1. Basic Concepts for Coulomb Systems.- 2.2. Survey of Exact Quantum-Mechanical Results for Coulomb Systems.- 2.3. Survey of Exact Quantum-Statistical Results for Macroscopic Coulomb Systems.- 3. Quantum Statistics of Many-Particle Systems.- 3.1. Elements of Quantum Statistics.- 3.1.1. Quantum Mechanics of Many-Particle Systems.- 3.1.2. The Method of Second Quantization.- 3.1.3. Quantum Statistics. Density Operator.- 3.1.4. Reduced Density Operators. Bogolyubov Hierarchy.- 3.1.5. The Classical Limit, BBGKY Hierarchy.- 3.1.6. Systems in Thermodynamical Equilibrium.- 3.2. The Method of Green’s Functions in Quantum Statistics.- 3.2.1. Definition of Green’s Functions.- 3.2.2. General Properties of the Correlation Function and One-Particle Green’s Function.- 3.2.3. Long Time Behaviour of Correlation Functions.- 3.2.4. Equation of Motion for the One-Particle Green’s Function. Self Energy.- 3.2.5. Dynamical and Thermodynamical Information Contained in the Spectral Function A(p, w).- 3.2.6. The Two-Particle Green’s Function.- 3.2.7. Equation of Motion for Higher Order Green’s Functions.- 3.2.8. The Binary Collision Approximation (Ladder Approximation).- 3.2.9. T-Matrix and Thermodynamic Properties in Binary Collision Approximation.- 3.3. Quantum Statistics of Charged Many-Particle Systems.- 3.3.1. Basic Equations. Screening.- 3.3.2. Analytic Properties of Vs and ?.- 3.3.3. The “Random Phase Approximation” RPA.- 4. Application of the Green’s Function Technique to Coulomb Systems.- 4.1. Types of Different Approximations.- 4.1.1. Diagram Representation of ? and ?.- 4.1.2. The RPA and the Vs-Approximation for the Self Energy.- 4.1.3. Many-Particle Complexes and T-Matrices.- 4.1.4. Cluster Formation and the Chemical Picture.- 4.1.5. Cluster Decomposition of the Self Energy.- 4.2. Dielectric Properties of Charged Particle Systems. Random Phase Approximation.- 4.2.1. Linear Response to External Perturbations. General Remarks.- 4.2.2. Properties of the RPA Dielectric Function.- 4.2.3. Plasma Oscillations (Plasmons).- 4.3. Single-Particle Excitations.- 4.3.1. Quasi-Particle Concept.- 4.3.2. Self Energy in Vs-Approximation.- 4.4. Two-Particle Properties in a Plasma.- 4.4.1. Bethe-Salpeter Equation for a Two-Particle Cluster.- 4.4.2. Solution of the Bethe-Salpeter Equation. Effective Wave Equation and Spectral Representations.- 4.4.3. Two-Particle States in the Dynamically Screened Ladder Approximation.- 4.4.4. Two-Particle States in Surrounding Medium in First Born Approximation.- 4.4.5. Numerical Results and Discussion of the Two-Particle States.- 4.5. Dielectric Function Including Bound States.- 4.5.1. Extended RPA Dielectric Function for a Partially Ionized Plasma.- 4.5.2. Limiting Behaviour of the Extended RPA Dielectric Function.- 4.5.3. Self Energy and Vertex Corrections to the Extended RPA Dielectric Function.- 4.5.4. Local Field Effects and Enhancement of the Dielectric Function.- 5. Equilibrium Properties in Classical and Quasiclassical Approximation.- 5.1. The One-Component Plasma Model.- 5.2. Many-Component Systems. Slater Sums.- 5.2.1. Partition Functions and Effective Potentials.- 5.2.2. Calculation of Slater Sums and Effective Potentials.- 5.3. The Pair Distribution Function.- 5.3.1. Basic Equations and Hierarchy.- 5.3.2. Discussion of the Pair Distribution.- 5.4. Thermodynamic Functions.- 5.4.1. Cluster Expansions of the Free Energy.- 5.4.2. Density Expansions of the Free Energy.- 6. Quantum-Statistical Calculations of Equilibrium Properties.- 6.1. Equation of State in the Screened Ladder Approximation.- 6.1.1. The Second Virial Coefficient.- 6.1.2. Evaluation of the Higher Order Contributions.- 6.1.3. Evaluation of the Hartree-Fock and the Montroll-Ward Contributions.- 6.2. Density and Chemical Potential in the Screened Ladder Approximation.- 6.2.1. Bound State and Quasiparticle Contributions.- 6.2.2. The Mass Action Law.- 6.3. One-Component Plasmas.- 6.3.1. Analytical Formulae for the Limiting Situations.- 6.3.2. Padé Interpolations between the Degenerate and the Nondegenerate Cases.- 6.3.3. Padé Approximations Including Higher Order Interaction Terms and Wigner Crystallization.- 6.4. Electron-Hole Plasmas.- 6.4.1. Analytical Results for the Plasma Model.- 6.4.2. Padé Approximations.- 6.4.3. Ionization Equilibrium.- 6.5. Hydrogen Plasmas.- 6.5.1. The Two-Fluid Model.- 6.5.2. Basic Formulae for the Limiting Situations and Padé Approximations.- 6.5.3. Ionization Equilibrium and Phase Diagram.- 6.6. Alkali Plasmas and Noble Gas Plasmas.- 6.6.1. Pseudopotentials.- 6.6.2. The Chemical Potential of the Neutral Component.- 6.6.3. The Chemical Potential of the Charged Component.- 6.6.4. Saha Equation and Ionization Equilibrium.- 7. Transport Properties.- 7.1. Linear Response Theory.- 7.1.1. Many-Body Effects and Transport Properties in Non-Ideal Plasmas.- 7.1.2. Transport Coefficients and Correlation Functions.- 7.1.3. Further Approaches.- 7.2. Evaluation of Collision Integrals Using Green’s Functions.- 7.2.1. Green’s Functions, Diagrams and Correlation Functions.- 7.2.2. Evaluation of Correlation Functions in First Born Approximation.- 7.2.3. Results for a Hydrogen Plasma.- 7.2.4. Inclusion of the Ionic Structure Factor.- 7.2.5. Dynamically Screened Second Born Approximation.- 7.2.6. Statically Screened T-Matrix Approximation. Results.- 7.3. Further Improvements of the Transport Theory.- 7.3.1. Self-Energy and Debye-Onsager Relaxation Effects.- 7.3.2. Hopping Conductivity.- 7.3.3. Concluding Remarks.- 8. Green’s Function Approach to Optical Properties.- 8.1. General Formalism.- 8.1.1. Many-Body Theory of Absorption Spectra.- 8.1.2. Dielectric Function and Spectral Line Shape of Plasmas.- 8.1.3. Doppler Broadening.- 8.2. Evaluation of Line Shift and Broadening.- 8.2.1. Explicit Expressions for Shift and Broadening.- 8.2.2. Relation to the Impact Approximation.- 8.2.3. Shift of Spectral Lines in Dense Hydrogen Plasmas.- 8.2.4. Estimation of the Shift and Broadening of Spectral Lines for an Argon Plasma.- 8.3. Further Approaches and Concluding Remarks.- 9. References.- 10. Subject Index.