Computational Statistical Physics From Billiards to Monte Carlo

In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

1 Game Theory and Statistical Mechanics.- 2 Chaotic Billiards.- 3 Combinatorial Optimization and High Dimensional Billiards.- 4 The Statistical Physics of Energy Landscapes: From Spin Glasses to Optimization.- 5 Optimization of Production Lines by Methods from Statistical Physics.- 6 Predicting and Generating Time Series by Neural Networks: An Investigation Using Statistical Physics.- 7 Statistical Physics of Cellular Automata Models for Traffic Flow.- 8 Self-Organized Criticality in Forest-Fire Models.- 9 Nonlinear Dynamics of Active Brownian Particles.- 10 Financial Time Series and Statistical Mechanics.- 11 ‘Go with the Winners’ Simulations.- 12 Aperiodicity and Disorder — Do They Play a Role?.- 13 Quantum Phase Transitions.- 14 Introduction to Energy Level Statistics.- 15 Randomness in Optical Spectra of Semiconductor Nanostructures.- 16 Characterization of the Metal—Insulator Transition in the Anderson Model of Localization.- 17 Percolation, Renormalization and Quantum Hall Transition.