Quantum Statistics of Charged Particle Systems

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.