| Game Theory and Statistical Mechanics | p. 1 |
| Introduction | p. 1 |
| Matrix Games | p. 2 |
| Nash Equilibria | p. 7 |
| Bimatrix Games | p. 9 |
| What Else? | p. 13 |
| References | p. 14 |
| Chaotic Billiards | p. 15 |
| Introduction | p. 15 |
| Billiard Systems | p. 17 |
| The Billiard Computer Program | p. 18 |
| Integrable Systems | p. 18 |
| Circular Billiards | p. 18 |
| Elliptical Billiards | p. 20 |
| 'Typical' Billiards | p. 22 |
| Further Computer Experiments | p. 26 |
| Uncertainty and Predictability | p. 26 |
| Fine Structure in Phase Space | p. 28 |
| Gravitational Billiards | p. 29 |
| Quantum Billiards | p. 31 |
| Appendixes | p. 32 |
| Billiard Mapping | p. 32 |
| Stability Map | p. 33 |
| Elliptical Billiard: Constant of Motion | p. 34 |
| References | p. 35 |
| Combinatorial Optimization and High Dimensional Billiards | p. 37 |
| Introduction | p. 37 |
| Billiards | p. 40 |
| Linear Programming | p. 42 |
| The Simplex Algorithm | p. 43 |
| The Internal Point Algorithms | p. 45 |
| The Billiard Algorithm I | p. 45 |
| The Billiard Algorithm II | p. 45 |
| Difficult (Integer) Linear Programming Problems | p. 46 |
| The Bayes Perceptron | p. 47 |
| The Geometry of Perceptrons | p. 49 |
| How to Play Billiards in Version Space | p. 51 |
| Bayesian Inference for the Mixture Assignment Problem | p. 53 |
| Conclusion | p. 55 |
| References | p. 55 |
| The Statistical Physics of Energy Landscapes: From Spin Glasses to Optimization | p. 57 |
| An Introduction to Energy Landscapes | p. 57 |
| Thermal Relaxation on Energy Landscapes | p. 58 |
| Markov Processes and the Metropolis Algorithm | p. 58 |
| Coarse-Graining Mountainous Landscapes | p. 60 |
| Coarse Graining on a Coarser Scale | p. 64 |
| Tree Dynamics | p. 65 |
| A Serious Application: Aging Effects in Spin Glasses | p. 66 |
| Stochastic Optimization: How to Find the Global Minimum in an Energy Landscape | p. 68 |
| Simulated Annealing | p. 69 |
| Threshold Accepting and Tsallis Annealing | p. 70 |
| Adaptive Schedules and the Ensemble Approach | p. 71 |
| Conclusion | p. 74 |
| References | p. 75 |
| Optimization of Production Lines by Methods from Statistical Physics | p. 77 |
| A Short Overview over Optimization Algorithms | p. 77 |
| Methods from Statistical Physics | p. 79 |
| A Simple Example: The Traveling Salesman Problem | p. 80 |
| Optimization with Constraints | p. 83 |
| The Linear Assembly Line Problem | p. 85 |
| The Problem | p. 85 |
| The Model | p. 86 |
| Computational Results | p. 87 |
| The Network Assembly Line Problem | p. 90 |
| The Problem | p. 90 |
| The Model | p. 92 |
| Computational Results | p. 93 |
| Conclusion | p. 94 |
| References | p. 96 |
| Predicting and Generating Time Series by Neural Networks: An Investigation Using Statistical Physics | p. 97 |
| Introduction | p. 97 |
| Learning from Random Sequences | p. 98 |
| Generating Sequences | p. 100 |
| Predicting Time Series | p. 103 |
| Predicting with 100% Error | p. 105 |
| Learning from Each Other | p. 107 |
| Competing in the Minority Game | p. 108 |
| Predicting Human Beings | p. 109 |
| Summary110 | |
| References | p. 111 |
| Statistical Physics of Cellular Automata Models for Traffic Flow | p. 113 |
| Introduction | p. 113 |
| Basic Measurements of Traffic Flow Simulations with CA Models | p. 114 |
| Fundamentals of the NaSch Model | p. 115 |
| TheVDRModel | p. 117 |
| Model with Anticipation | p. 121 |
| Discussion and Conclusion | p. 123 |
| Appendix: Simulating Pedestrian Dynamics and Evacuation Processes | p. 124 |
| References | p. 126 |
| Self-Organized Criticality in Forest-Fire Models | p. 127 |
| Introduction | p. 127 |
| The Spiral State and the SOC State | p. 128 |
| Properties of the SOC State | p. 128 |
| FFM with the Tree Density as Parameter | p. 131 |
| Removal of Tree Clusters | p. 131 |
| One-by-One Removal of Trees | p. 132 |
| Conclusion | p. 132 |
| Appendixes | p. 133 |
| Exact Results in One Dimension | p. 133 |
| Mean Field Theory | p. 136 |
| Immunity | p. 138 |
| References | p. 139 |
| Nonlinear Dynamics of Active Brownian Particles | p. 141 |
| Introduction | p. 141 |
| Equations of Motion, Friction and Forces | p. 142 |
| Two-Dimensional Dynamics | p. 144 |
| Conclusion | p. 150 |
| References | p. 151 |
| Financial Time Series and Statistical Mechanics | p. 153 |
| Introduction | p. 153 |
| Phase, Amplitude and Frequency Revisited | p. 155 |
| Coherence | p. 155 |
| Roughness | p. 155 |
| Persistence | p. 156 |
| Power Law Exponents | p. 156 |
| Persistence and Spectral Density | p. 156 |
| Roughness, Fractal Dimension, Hurst Exponent, and Detrended Fluctuation Analysis | p. 159 |
| Conclusion | p. 162 |
| Appendixes | p. 164 |
| Moving Averages | p. 164 |
| Discrete Scale Invariance | p. 164 |
| References | p. 166 |
| 'Go with the Winners' Simulations | p. 169 |
| Introduction | p. 169 |
| An Example: A Lamb in front of a Pride of Lions | p. 170 |
| Other Examples | p. 173 |
| Multiple Spanning Percolation Clusters | p. 173 |
| Polymers | p. 176 |
| Lattice Animals (Randomly Branched Polymers) | p. 180 |
| Implementation Details.181 | |
| Depth First Versus Breadth First | p. 182 |
| Choosing W± | p. 183 |
| Choosing the Bias | p. 183 |
| Error Estimates and Reliability Tests | p. 185 |
| Diffusion Quantum Monte Carlo | p. 187 |
| Conclusion | p. 188 |
| References | p. 18911 |
| Introduction | p. 191 |
| The Ising Model | p. 193 |
| The Square-Lattice Ising Model | p. 193 |
| Phase Transitions and Critical Exponents | p. 194 |
| The Ising-Model Phase Transition | p. 196 |
| The Ising Quantum Chain | p. 197 |
| Effects of Disorder: Some General Remarks | p. 197 |
| Heuristic Scaling Arguments | p. 198 |
| Random Ising Models | p. 200 |
| Aperiodic Ising Models | p. 201 |
| Aperiodic Tilings on the Computer | p. 201 |
| Ising Models on Planar Aperiodic Graphs | p. 204 |
| Aperiodic Ising Quantum Chains | p. 207 |
| Summary and Conclusions | p. 208 |
| References | p. 209 |
| Quantum Phase Transitions | p. 211 |
| Introduction: From the Melting of Ice to Quantum Criticality | p. 211 |
| Basic Concepts of Phase Transitions and Critical Behavior | p. 214 |
| How Important is Quantum Mechanics? | p. 217 |
| Quantum Critical Points | p. 220 |
| Example: Transverse Field Ising Model | p. 221 |
| Quantum Phase Transitions and Non-Fermi Liquids | p. 224 |
| Summary and Outlook | p. 226 |
| References | p. 226 |
| Introduction to Energy Level Statistics | p. 227 |
| Introduction 227 | |
| Statistics of Energy Levels | p. 228 |
| Level Spacing Distribution | p. 230 |
| Level Repulsion and Symmetry | p. 231 |
| Gaussian Ensembles | p. 233 |
| Level Spacing Distribution at the Anderson Transition | p. 236 |
| Fluctuations of Energy Levels of Quantum Dots | p. 238 |
| Conclusion239 | |
| References | p. 239 |
| Randomness in Optical Spectra of Semiconductor Nanostructures | p. 241 |
| Spectra of Semiconductor Nanostructures | p. 241 |
| Anderson Model, Wavefunction Localization, and Mobility Edge | p. 243 |
| Remarks on Macroscopic Spectra | p. 247 |
| Repulsion of Energy Levels | p. 248 |
| Microscopic Relaxation Kinetics | p. 250 |
| Radiative-Lifetime Distribution | p. 251 |
| Rayleigh Scattering, Speckles, and Enhanced Back-Scattering | p. 252 |
| Summary | p. 255 |
| References | p. 256 |
| Characterization of the Metal-Insulator Transition in the Anderson Model of Localization | p. 259 |
| The Metal-Insulator Transition in Disordered Systems | p. 259 |
| The Transfer Matrix Method | p. 262 |
| Multifractal Analysis | p. 268 |
| Energy Level Statistics | p. 272 |
| References | p. 277 |
| Percolation, Renormalization and Quantum Hall Transition | p. 279 |
| Introduction | p. 279 |
| Percolation | p. 280 |
| The Physics of Connectivity | p. 280 |
| The Coloring Algorithm | p. 282 |
| The Growth Algorithm | p. 283 |
| The Frontier Algorithm | p. 283 |
| Real-Space Renormalization | p. 285 |
| Making Use of Self-Similarity | p. 285 |
| Monte Carlo RG | p. 286 |
| The Quantum Hall Effect | p. 287 |
| Basics of the IQHE | p. 287 |
| RG for the Chalker-Coddington Network Model | p. 289 |
| Conductance Distributions at the QH Transition | p. 291 |
| Summary and Conclusions | p. 293 |
| References | p. 293 |
| Index | p. 295 |
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