Bonitz Quantum Kinetic Theory

2. Auflage 2016
ISBN: 978-3-319-24121-0
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 412 Seiten, eBook

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

Zielgruppe

Research

Autoren/Hrsg.

Bonitz, Michael

Inhaltsverzeichnis

1;Preface to the Second Edition;5
2;Preface to the First Edition;7
3;Contents;10
4;Symbols;16
5;1 Introduction;18
5.1;1.1 Correlated Many-Particle Systems;19
5.2;1.2 Thermodynamic Properties of Correlated Systems;26
5.3;1.3 Ultrafast Nonequilibrium Phenomena;29
5.3.1;1.3.1 Dynamics of Isolated Systems;30
5.3.2;1.3.2 Interaction of Matter with Short Laser Pulses;31
5.3.3;1.3.3 Overview of Relaxation Processes;35
5.4;1.4 The Boltzmann Equation--Successes and Failure;37
5.4.1;1.4.1 An Elementary Introduction to the Boltzmann Equation;37
5.4.2;1.4.2 Unphysical Ultrafast Relaxation in Charged Particle Systems;40
5.5;1.5 Improved Theoretical Concepts;41
5.5.1;1.5.1 Outline of this Book;43
5.6;1.6 Problems;44
6;2 The Method of Reduced Density Operators;45
6.1;2.1 Density Operator. Von Neumann Equation;45
6.2;2.2 BBGKY-Hierarchy;48
6.2.1;2.2.1 Reduced Density Operators. Equations of Motion;48
6.2.2;2.2.2 Conservation Laws;53
6.3;2.3 Basic Representations of the Hierarchy;57
6.3.1;2.3.1 Coordinate Representation;57
6.3.2;2.3.2 Wigner Representation;59
6.3.3;2.3.3 Classical Limit and Quantum Corrections;61
6.3.4;2.3.4 Spatially Homogeneous Systems. Momentum Representation;62
6.4;2.4 Multi-component and Multi-band Systems;66
6.4.1;2.4.1 Bloch Representation of the Hierarchy;68
6.4.2;2.4.2 Remarks on General Properties of the BBGKY-Hierarchy;71
6.5;2.5 Correlations in Many-Particle Systems;72
6.5.1;2.5.1 BBGKY-Hierarchy for Correlation Operators;72
6.5.2;2.5.2 Energy Conservation Condition in Terms of Correlation Operators;74
6.6;2.6 Decoupling of the BBGKY-Hierarchy;75
6.6.1;2.6.1 Correlation Effects;78
6.6.2;2.6.2 *Selfenergy Effects;81
6.7;2.7 Relation to Equilibrium Correlation Functions;83
6.8;2.8 Problems;85
7;3 *Correlations Due to the Spin Statistics;86
7.1;3.1 (Anti-)Symmetrization of the Density Operators;88
7.2;3.2 Exchange and Phase Space Filling Effects;89
7.3;3.3 (Anti-)Symmetrization of the First and Second Hierarchy Equations;92
7.4;3.4 (Anti-)Symmetrization of the Third Hierarchy Equation;93
7.4.1;3.4.1 (Anti-)Symmetrization of the Selfenergy Terms;94
7.4.2;3.4.2 Energy Conservation with Spin Statistics;95
7.5;3.5 Problems;97
8;4 Mean--Field Approximation. Quantum Vlasov Equation. Collective Effects;98
8.1;4.1 Linearization of the Quantum Vlasov Equation. Dielectric Function;100
8.2;4.2 Collective Plasma Excitations (Plasmons);107
8.3;4.3 Plasma Instabilities;110
8.4;4.4 Examples: Plasmons in Quantum Systems;113
8.4.1;4.4.1 One-Dimensional Quantum Plasmas;114
8.4.2;4.4.2 Plasmons in 2D and 3D Quantum Systems;121
8.5;4.5 *Quasilinear Theory for Classical and Quantum Systems;124
8.6;4.6 Numerical Solutions of the Nonlinear Quantum Vlasov Equation;128
8.7;4.7 *Kinetic Equations for Carrier--Plasmon Interaction;129
8.8;4.8 Problem;132
9;5 Correlations and Their Dynamics;133
9.1;5.1 Hierarchy of Relaxation Processes. Time Scale Separation;134
9.2;5.2 Correlation Buildup. Correlation Time Approximation;137
10;6 Correlation Dynamics and Non-Markovian Effects;140
10.1;6.1 Solution for g12 in Second Born Approximation;141
10.2;6.2 Non-Markovian Quantum Landau Equation;143
10.3;6.3 Markov Limit;145
10.4;6.4 Non-Markovian Quantum Landau Equation with Exchange Renormalization and Time-Dependent Fields;147
10.5;6.5 Problems;152
11;7 Non-Markovian Kinetic Equations with Selfenergy;153
11.1;7.1 *Selfenergy in Density Operator Approach;154
11.2;7.2 Renormalized Binary Correlation Operator;158
11.3;7.3 Non-Markovian Quantum Landau Equation with Selfenergy;160
11.3.1;7.3.1 Properties of the Landau Equation. Memory Effects;161
11.3.2;7.3.2 Dynamics of Physical Observables. Energy Conservation;166
11.3.3;7.3.3 Markov Limit and Corrections. Retardation Expansion;170
11.3.4;7.3.4 *Approximations for the Selfenergy;175
11.4;7.4 *Discussion of the Selfenergy Concept. Relation to Green Functions Results;178
11.5;7.5 Problem;181
12;8 Properties of the Quantum Kinetic Equation;182
12.1;8.1 Markovian Dynamics of Macroscopic Observables;183
12.2;8.2 Irreversibility. H-Theorem. Equilibrium Solution of the Markovian Kinetic Equation;184
12.3;8.3 Equilibrium Correlations;187
12.4;8.4 Non-Markovian Dynamics of Macroscopic Observables;188
12.5;8.5 Total Energy Conservation in Non-Markovian Kinetics;190
12.6;8.6 H-Theorem in Non-Markovian Kinetics;191
12.7;8.7 Problems;193
13;9 Strong Coupling Effects. Ladder (T-Matrix) Approximation;194
13.1;9.1 Generalized Binary Collision Approximation;195
13.2;9.2 *Selfenergy in Ladder (T-Matrix) Approximation;196
13.3;9.3 Correlation Operator in Binary Collision Approximation;198
13.3.1;9.3.1 Propagators and Scattering Quantities;198
13.3.2;9.3.2 Møller Operators and T-Operators;201
13.3.3;9.3.3 Correlation Operator in Binary Collision Approximation;203
13.3.4;9.3.4 *Gradient Expansion of g12 and Physical Observables;206
13.3.5;9.3.5 *Recovery of the Generalized Kadanoff-Baym Ansatz;209
13.4;9.4 Collision Integral with Memory Effects;210
13.5;9.5 Kinetic Equation in First Order Gradient Expansion;213
13.6;9.6 Numerical Results and Discussion;217
13.6.1;9.6.1 Markovian T-Matrix Scattering Rates;218
13.6.2;9.6.2 Summary and Comments on the T-Matrix Approximation;220
13.6.3;9.6.3 Numerical Results for Lattice Systems;220
14;10 *Random Phase Approximation;222
14.1;10.1 Generalized Polarization Approximation: Selfenergy;223
14.2;10.2 Dynamical Screening in Nonequilibrium;227
14.3;10.3 Non-Markovian Balescu-Lenard Equation;232
14.3.1;10.3.1 Properties of the Non-Markovian Balescu-Lenard Equation. Markov Limit;233
14.3.2;10.3.2 Correlation Energy in RPA;237
14.3.3;10.3.3 Short-Time Behavior: Screening Buildup;238
14.4;10.4 Problem;240
15;11 *Dynamically Screened Ladder Approximation;241
15.1;11.1 Generalized Screened Ladder Approximation. Selfenergy;242
15.1.1;11.1.1 Limiting Cases of the Screened Ladder Approximation;245
15.2;11.2 Gould--DeWitt Approximation;246
16;12 Charged Many-Particle Systems in Electromagnetic Fields. Generalized Bloch Equations;247
16.1;12.1 Field-Matter Interaction;248
16.2;12.2 Field Effects on the Distribution and the Propagators;252
16.3;12.3 Interaction of Optical Fields with Multiband Systems;259
16.4;12.4 Bloch Representation of the First Hierarchy Equation;262
16.5;12.5 *Bloch Representation of the Solution g12(t);269
16.6;12.6 *Correlation Operator, Non-Markovian Collision Integral and Selfenergy in an Electromagnetic Field;274
16.7;12.7 *Non-Markovian Bloch Equations Beyond the Static Born Approximation;277
16.8;12.8 Problem;280
17;13 *Nonequilibrium Green Functions Approach to Field-Matter Dynamics;281
17.1;13.1 Introduction;282
17.2;13.2 Basic Concepts of Relativistic Quantum Electrodynamics;283
17.2.1;13.2.1 Field Operators of the Maxwell Field;284
17.2.2;13.2.2 Relativistic Field Operators for Fermions;284
17.2.3;13.2.3 Statistical Description in Nonequilibrium;286
17.2.4;13.2.4 Green Functions for Photons and Charge Carriers;288
17.3;13.3 Relativistic Keldysh-Kadanoff-Baym Equations for Particles and Photons;292
17.4;13.4 Approximations for the Selfenergies;294
17.4.1;13.4.1 Expansion in Terms of G0 and D;295
17.4.2;13.4.2 Expansion in Terms of G and D;298
17.4.3;13.4.3 Adiabatic Approximation for the Electromagnetic Field;298
17.5;13.5 Nonrelativistic Keldysh-Kadanoff-Baym Equations;300
17.5.1;13.5.1 Nonrelativistic Limit. Pauli Equation;300
17.5.2;13.5.2 Green Functions for Carriers, Photons and Plasmons;302
17.5.3;13.5.3 Keldysh-Kadanoff-Baym Equations for Carriers, Plasmons and Photons;305
17.6;13.6 Particle Keldysh-Kadanoff-Baym Equations. Properties and Approximations;305
17.6.1;13.6.1 Approximations for the Selfenergy;307
17.6.2;13.6.2 Properties of the Keldysh-Kadanoff-Baym Equations;309
17.6.3;13.6.3 Numerical Results;311
17.7;13.7 Interband KBE;314
17.7.1;13.7.1 Two-Time Semiconductor Bloch Equations;315
17.7.2;13.7.2 Illustration: NEGF-Simulation for Laser Excitation of Electrons in a Harmonic Oscillator;317
17.7.3;13.7.3 Numerical Results for Ultrafast Relaxation of Femtosecond-Laser Excited Semiconductors;320
17.7.4;13.7.4 Computing Optical Absorption Via Solution of the Interband KBE;323
17.8;13.8 Nonequilibrium KBE-Approach to Equilibrium Response Properties;326
17.8.1;13.8.1 Response Properties in Lowest Order (Linear Response);327
17.8.2;13.8.2 Relation Between the Two-Particle Kernel ? and the KBE-Selfenergy ?;328
17.8.3;13.8.3 Interband Approach to Plasma Oscillations of the Correlated Electron Gas;329
17.8.4;13.8.4 Optical Absorption of Atoms and Molecules. Electronic Double Excitations;331
17.9;13.9 Kinetic Equations for Single-Time Functions. Comparison to Density Operators;333
17.10;13.10 Build Up of Dynamical Screening;338
17.10.1;13.10.1 Theoretical Approaches to the Screening Dynamics;338
17.10.2;13.10.2 Femtosecond Buildup of the RPA Dielectric Function;339
17.10.3;13.10.3 Selfconsistent Solution of the KBE in RPA;341
17.10.4;13.10.4 Experimental Results. Outlook;341
17.11;13.11 Problems;343
18;14 Conclusion;344
19;Appendix AUsed Mathematical Formulas;346
20;Appendix BWigner Representationof the BBGKY-Hierarchy;350
21;Appendix CEquations of Motion for Binaryand Ternary Correlations;354
22;Appendix DProperties of the FreePropagators U0 and U0±;361
23;Appendix ERetardation Expansion;365
24;Appendix FNumerical Solution of Quantum KineticEquations;371
25;Appendix GSolutions to Problems;382
26; References;391
27;Index;407

Introduction.- Reduced Density Operators.- Correlations due to the Spin Statistics.- Mean-Field Approximation.- Correlations and their Dynamics.- Non-Markovian Effects.- Kinetic Equations with Selfenergy.- Properties of the Kinetic Equation.- T-Matrix Approximation.- Random Phase Approximation.- Screened Ladder Approximation.- Charged Carriers in EM Fields.- Non-Equilibrium Green’s Functions.- Kinetics vs. Molecular Dynamics.- Conclusion.