Complicated many-particle problems abound in nature and in research alike. Plasma physics, statistical physics and condensed matter physics, as primary examples, are all heavily dependent on efficient methods for solving such problems. Addressing graduate students and young researchers, this book presents an overview and introduction to state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers.
Author(s): Ralf Schneider, Amit Raj Sharma, Abha Rai (auth.), H. Fehske, R. Schneider, A. Weiße (eds.)
Series: Lecture Notes in Physics 739
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2008
Language: English
Pages: 780
City: Berlin; New York
Tags: Mathematical and Computational Physics;Nuclear Physics, Heavy Ions, Hadrons
Front Matter....Pages I-XV
Front Matter....Pages 1-1
Introduction to Molecular Dynamics....Pages 3-40
Wigner Function Quantum Molecular Dynamics....Pages 41-60
Front Matter....Pages 61-61
The Monte Carlo Method, an Introduction....Pages 63-78
Monte Carlo Methods in Classical Statistical Physics....Pages 79-140
The Monte Carlo Method for Particle Transport Problems....Pages 141-158
Front Matter....Pages 159-159
The Particle-in-Cell Method....Pages 161-189
Gyrokinetic and Gyrofluid Theory and Simulation of Magnetized Plasmas....Pages 191-219
Front Matter....Pages 221-221
Boltzmann Transport in Condensed Matter....Pages 223-254
Semiclassical Description of Quantum Many-Particle Dynamics in Strong Laser Fields....Pages 255-273
Front Matter....Pages 275-275
World-line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons....Pages 277-356
Autocorrelations in Quantum Monte Carlo Simulations of Electron-Phonon Models....Pages 357-366
Diagrammatic Monte Carlo and Stochastic Optimization Methods for Complex Composite Objects in Macroscopic Baths....Pages 367-395
Path Integral Monte Carlo Simulation of Charged Particles in Traps....Pages 397-412
Front Matter....Pages 413-413
Ab-Initio Approach to the Many-Electron Problem....Pages 415-436
Ab-Initio Methods Applied to Structure Optimization and Microscopic Modelling....Pages 437-469
Front Matter....Pages 471-471
Dynamical Mean-Field Approximation and Cluster Methods for Correlated Electron Systems....Pages 473-503
Local Distribution Approach....Pages 505-526
Front Matter....Pages 527-527
Exact Diagonalization Techniques....Pages 529-544
Chebyshev Expansion Techniques....Pages 545-577
Front Matter....Pages 579-579
The Conceptual Background of Density-Matrix Renormalization....Pages 581-596
Front Matter....Pages 579-579
Density-Matrix Renormalization Group Algorithms....Pages 597-619
Dynamical Density-Matrix Renormalization Group....Pages 621-635
Studying Time-Dependent Quantum Phenomena with the Density-Matrix Renormalization Group....Pages 637-652
Applications of Quantum Information in the Density-Matrix Renormalization Group....Pages 653-664
Density-Matrix Renormalization Group for Transfer Matrices: Static and Dynamical Properties of 1D Quantum Systems at Finite Temperature....Pages 665-677
Front Matter....Pages 679-679
Architecture and Performance Characteristics of Modern High Performance Computers....Pages 681-730
Optimization Techniques for Modern High Performance Computers....Pages 731-767
Back Matter....Pages 769-780
