Introduction to Computational Methods in Many Body Physics
eds. Michael Bonitz and Dirk Semkat
416 pages 10x7 inches
Jan 2006 Hardcover
ISBN 1-58949-009-6

This book presents an introduction to some of the most advanced and powerful numerical methods currently available to simulate many-particle systems. The problems treated include equilibrium and nonequilibrium properties of systems (both classical and quantum) and the interaction of charged particles with electromagnetic fields. Among the computational methods  presented are classical and path integral Monte Carlo, classical, quantum and relativistic kinetic equations, quantum molecular dynamics, particle in cell simulations and time-dependent density functional theory. Written by experts in computational physics and specialists in a variety of fields, this introductory book has almost everything needed to start programming, with many little details that are usually omitted in original literature.

graduate students, teachers, researchers, engineers, who are interested in numerical modeling. 


Chapter 1.   Introduction (by Michael Bonitz)
1.1 Preliminary remarks
1.2 Density operator Von Neumann equation
1.3 Solution of the von Neumann/Liouville equation
1.4 BBGKY-hierarchy
1.5 Basic representations of the hierarchy
1.6 Relation to equilibrium correlation functions

Part I: Dynamics of Classical Many-particle Systems
Chapter 2.   Classical Particle Simulations (by  Hartmut Ruhl)
2.1 Synopsis
2.2 Introduction
2.3 The physics model
2.4 The numerical approach
2.5 The simulation code PSC
2.6 Examples
2.7 Summary
2.8 The open source project PSC

Part II: Correlated Quantum Systems in Equilibrium and Nonequilibrium
Chapter 3.  Density Functional Theory  (by George F. Bertsch and Kazuhiro Yabana)
3.1 Introduction
3.2 What is density functional theory?
3.3 Kohn-Sham theory
3.4 Numerical methods for the Kohn-Sham equation
3.5 Some applications and limitations of DFT
3.6 Limitations of DFT
3.7 Time-dependent density functional theory: the equations
3.8 TDDFT: numerical aspects
3.9 Applications of TDDFT

Chapter 4.  Generalized Quantum Kinetic Equations (by Dirk Semkat and Michael Bonitz)
4.1 Introduction
4.2 Idea of second quantization
4.3 Real-time Green's functions
4.4 Derivation of the Kadanoff-Baym/Keldysh equations
4.5 Single-time kinetic equations
4.6 Numerical procedure
4.7 Numerical Results
4.8 Interband Kadanoff-Baym equations
4.9 Survey of numerical applications to other systems
Appendix: self-energy in T-matrix approximation

Part III: First-principle Approaches to Correlated Quantum Systems  
Chapter 5.  Classical and Quantum Monte Carlo Methods (by Alexei Filinov and Michael Bonitz)
5.1 Classical systems and the Monte Carlo method
5.2 Path Integral Monte Carlo

Chapter 6.  Quantum Molecular Dynamics (by Alexei Filinov, Vladimir Filinov, Yurii Lozovik and Michael Bonitz)
6.1 Introduction
6.2 Quantum distribution functions
6.3 Quantum dynamics I: Method of Wigner trajectories
6.4 Quantum dynamics II: Monte Carlo approach to ensembles of quantum trajectories
6.5 Wigner function in the canonical ensemble

Access to program examples

Subject Index

All authors are theoretical physicists with extensive experience in Many-Body Physics and in Computational Physics.

George Bertsch works in quantum many-particle theory, nuclear physics, clusters, nanoscale electronic systems. He is one of the pioneers of time-dependent density functional theory. He is a full professor and senior fellow at the Physics Department of the University of Washington, Seattle. He has been the editor of the Reviews of Modern Physics for many years. Among his many honors are the 2004 Bonner prize of the APS and a honorary doctoral degree of the University of Milan.

Michael Bonitz (born 1960) has expertise in plasma physics, semiconductor physics, statistical physics. He is a C4-professor at the University Kiel, Germany. He is recipient of the Gustav Hertz Prize of the German Physical Society and author and editor of five books on classical and quantum kinetic theory.

Alexei Filinov (born 1975) received his PhD for a thesis on quantum Monte Carlo and quantum Molecular Dynamics Simulations. He is a Research Assistant at Kiel University at the Chair of Michael Bonitz.

Vladimir Filinov (born 1944) was among the first who applied path integral Monte Carlo methods in plasma physics. He developed an original method of Wigner function quantum Molecular Dynamics. He is group leader at the High Energy Density Institute of the Russian Academy of Sciences, Moscow, author of a monograph, co-author of three books and was visiting professor at Rostock University.

Yurii Lozovik (born 1937) is a leading expert in solid state physics, in particular semiconductor physics. He is a full professor at the Moscow Physical-Technical University and Department head at the Institute of Spectroscopy of the Russian Academy of Sciences in Troitsk, Moscow Region. He is co-author of seven books.

Hartmut Ruhl (born 1963) is an expert in plasma physics and high intensity laser-matter interaction. He has pioneered relativistic Vlasov simulations and full three-dimensional relativistic particle-in-cell simulations of plasmas. He is a C3-professor at the Ruhr University Bochum, Germany.

Dirk Semkat (born 1973) received his PhD for a thesis on Nonequilibrium Green's functions. He works in plasma physics and quantum kinetic theory at Rostock University, Germany.

Kazuhiro Yabana (born 1960) works in computational many-particle physics, nuclear physics, atomic and molecular physics, and optical science. He is a full professor at the Center for Computational Sciences of the University of Tsukuba. He has pioneered a real-time, real-space electron dynamics simulation in the time-dependent density-functional theory.