Quantum Statistics of Nonideal Plasmas (eBook)

Preface 6
Table of Contents 8
1. Introduction 13
2. Introduction to the Physics of Nonideal Plasmas 19
2.1 The Microscopic and Statistical Description of a Fully Ionized Plasma 19
2.2 Equilibrium Distribution Function. Degenerate and Non- degenerate Plasmas 22
2.3 The Vlasov Equation 26
2.4 Dynamical Screening 29
2.5 Self-Energy and Stopping Power 35
2.6 Thermodynamic Properties of Plasmas. The Plasma Phase Transition 38
2.7 Bound States in Dense Plasmas. Lowering of the Ionization Energy 43
2.8 Ionization Equilibrium and Saha Equation. The Mott- Transition 47
2.9 The Density–Temperature Plane 52
2.10 Boltzmann Kinetic Equation 55
2.11 Transport Properties 58
2.12 Ionization Kinetics 69
3. Quantum Statistical Theory of Charged Particle Systems 77
3.1 Quantum Statistical Description of Plasmas 77
3.2 Method of Green’s Functions 82
3.3 Equations of Motion for Correlation Functions and Green’s Functions 95
3.4 Green’s Functions and Physical Properties 115
4. Systems with Coulomb Interaction 129
4.1 Screened Potential and Self-Energy 129
4.2 General Response Functions 132
4.3 The Kinetics of Particles and Screening. Field Fluctuations 135
4.4 The Dielectric Function of the Plasma. General Properties, Sum Rules 142
4.5 The Random Phase Approximation (RPA) 148
4.6 Excitation Spectrum, Plasmons 160
4.7 Fluctuations, Dynamic Structure Factor 166
4.8 Static Structure Factor and Radial Distribution Function 173
4.9 Dielectric Function Beyond RPA 175
4.10 Equations of Motion for Density–Density Correlation Functions. Schrödinger Equation for Electron– Hole Pairs 177
4.11 Self-Energy in RPA. Single-Particle Spectrum 182
5. Bound and Scattering States in Plasmas. Binary Collision Approximation 191
5.1 Two-Time Two-Particle Green’s Function 191
5.2 Bethe–Salpeter Equation in Dynamically Screened Ladder Approximation 197
5.3 Bethe–Salpeter Equation for a Statically Screened Potential 201
5.4 Effective Schrödinger Equation. Bilinear Expansion 204
5.5 The T -Matrix 208
5.6 Two-Particle Scattering in Plasmas. Cross Sections 217
5.7 Self-Energy and Kadanoff–Baym Equations in Ladder Approximation 221
5.8 Dynamically Screened Ladder Approximation 224
5.9 The Bethe–Salpeter Equation in Local Approximation. Thermodynamic Equilibrium 230
5.10 Perturbative Solutions. Effective Schrödinger Equation 235
5.11 Numerical Results 239
6. Thermodynamics of Nonideal Plasmas 249
6.1 Basic Equations 249
6.2 Screened Ladder Approximation 252
6.3 Ring Approximation for the EOS. Montroll– Ward Formula 254
6.4 Next Order Terms 272
6.5 Equation of State in Ladder Approximation. Bound States 276
6.6 Thermodynamic Properties of the H-Plasma 315
6.7 The Dense Partially Ionized H-Plasma 337
7. Nonequilibrium Nonideal Plasmas 349
7.1 Kadanoff–Baym Equations. Ultra- fast Relaxation in Dense Plasmas 349
7.2 The Time-Diagonal Kadanoff–Baym Equation 354
7.3 The Quantum Landau Equation 359
7.4 Dynamical Screening, Generalized Lenard– Balescu Equation 365
7.5 Particle Kinetics and Field Fluctuations. Plasmon Kinetics 369
7.6 Kinetic Equation in Ladder Approximation. Boltzmann Equation 376
7.7 Bound States in the Kinetic Theory 382
7.8 Hydrodynamic Equations 393
8. Transport and Relaxation Processes in Nonideal Plasmas 397
8.1 Rate Equations and Reaction Rates 397
8.2 Relaxation Processes 415
8.3 Quantum Kinetic Theory of the Stopping Power 428
9. Dense Plasmas in External Fields 447
9.1 Plasmas in Electromagnetic Fields 447
9.2 The Static Electrical Conductivity 480
References 515
Index 533