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Bibliografická citace

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0 (hodnocen0 x )
BK
First published
Oxford : Oxford University Press, 2006
xii, 342 stran : ilustrace ; 25 cm

objednat
ISBN 978-0-19-851536-4 (brožováno)
Oxford master series in statistical, computational, and theoretical physics ; 13
Obsahuje bibliografie a rejstřík
001461706
Contents // 1 Monte Carlo methods 1 // 1.1 Popular games in Monaco 3 // 1.1.1 Direct sampling 3 // 1.1.2 Markov-chain sampling 4 // 1.1.3 Historical origins 9 // 1.1.4 Detailed balance 15 // 1.1.5 The Metropolis algorithm 21 // 1.1.6 A priori probabilities, triangle algorithm 22 // 1.1.7 Perfect sampling with Markov chains 24 // 1.2 Basic sampling 27 // 1.2.1 Real random numbers 27 // 1.2.2 Random integers, permutations, and combinations 29 // 1.2.3 Finite distributions 33 // 1.2.4 Continuous distributions and sample transformation 35 // 1.2.5 Gaussians 37 // 1.2.6 Random points in/on a sphere 39 // 1.3 Statistical data analysis 44 // 1.3.1 Sum of random variables, convolution 44 // 1.3.2 Mean value and variance 48 // 1.3.3 The central limit theorem 52 // 1.3.4 Data analysis for independent variables 55 // 1.3.5 Error estimates for Markov chains 59 // 1.4 Computing 62 // 1.4.1 Ergodicity 62 // 1.4.2 Importance sampling 63 // 1.4.3 Monte Carlo quality control 68 // 1.4.4 Stable distributions 70 // 1.4.5 Minimum number of samples 76 // Exercises 77 // References 79 // Hard disks and spheres 81 // 2.1 Newtonian deterministic mechanics 83 // 2.1.1 Pair collisions and wall collisions 83 // 2.1.2 Chaotic dynamics 86 // 2.1.3 Observables 87 // 2.1.4 Periodic boundary conditions 90 // 2.2 Boltzmann’s statistical mechanics 92 // 2.2.1 Direct disk sampling 95 // 2.2.2 Partition function for hard disks 97 // 2.2.3 Markov-chain hard-sphere algorithm 100 // 2.2.4 Velocities:
the Maxwell distribution 103 // 2.2.5 Hydrodynamics: long-time tails 105 // 2.3 Pressure and the Boltzmann distribution 108 // 2.3.1 Bath-and-plate system 109 // 2.3.2 Piston-and-plate system 111 // 2.3.3 Ideal gas at constant pressure 113 // 2.3.4 Constant-pressure simulation of hard spheres 115 // 2.4 Large hard-sphere systems 119 // 2.4.1 Grid/cell schemes 119 // 2.4.2 Liquid-solid transitions 120 // 2.5 Cluster algorithms 122 // 2.5.1 Avalanches and independent sets 123 // 2.5.2 Hard-sphere cluster algorithm 125 // Exercises 128 // References 130 // 3 Density matrices and path integrals 131 // 3.1 Density matrices 133 // 3.1.1 The quantum harmonic oscillator 133 // 3.1.2 Free density matrix 135 // 3.1.3 Density matrices for a box 137 // 3.1.4 Density matrix in a rotating box 139 // 3.2 Matrix squaring 143 // 3.2.1 High-temperature limit, convolution 143 // 3.2.2 Harmonic oscillator (exact solution) 145 // 3.2.3 Infinitesimal matrix products 148 // 3.3 The Feynman path integral 149 // 3.3.1 Naive path sampling 150 // 3.3.2 Direct path sampling and the Lévy construction 152 // 3.3.3 Periodic boundary conditions, paths in a box 155 // 3.4 Pair density matrices 159 // 3.4.1 Two quantum hard spheres 160 // 3.4.2 Perfect pair action 162 // 3.4.3 Many-particle density matrix 167 // 3.5 Geometry of paths 168 // 3.5.1 Paths in Fourier space 169 // 3.5.2 Path maxima, correlation functions 174 // 3.5.3 Classical random paths 177 // Exercises 182 // References 184 // 4 Bosons 185
4.1 Ideal bosons (energy levels) 187 // 4.1.1 Single-particle density of states 187 // 4.1.2 Trapped bosons (canonical ensemble) 190 // 4.1.3 Trapped bosons (grand canonical ensemble) 196 // 4.1.4 Large-iV limit in the grand canonical ensemble 200 // 4.1.5 Differences between ensembles—fluctuations 205 // 4.1.6 Homogeneous Bose gas 206 // 4.2 The ideal Bose gas (density matrices) 209 // 4.2.1 Bosonic density matrix 209 // 4.2.2 Recursive counting of permutations 212 // 4.2.3 Canonical partition function of ideal bosons 213 // 4.2.4 Cycle-length distribution, condensate fraction 217 // 4.2.5 Direct-sampling algorithm for ideal bosons 219 // 4.2.6 Homogeneous Bose gas, winding numbers 221 // 4.2.7 Interacting bosons 224 // Exercises 225 // References 227 // 5 Order and disorder in spin systems 229 // 5.1 The Ising model—exact computations 231 // 5.1.1 Listing spin configurations 232 // 5.1.2 Thermodynamics, specific heat capacity, and magnetization 234 // 5.1.3 Listing loop configurations 236 // 5.1.4 Counting (not listing) loops in two dimensions 240 // 5.1.5 Density of states from thermodynamics 247 // 5.2 The Ising model—Monte Carlo algorithms 249 // 5.2.1 Local sampling methods 249 // 5.2.2 Heat bath and perfect sampling 252 // 5.2.3 Cluster algorithms 254 // 5.3 Generalized Ising models 259 // 5.3.1 The two-dimensional spin glass 259 // 5.3.2 Liquids as Ising-spin-glass models 262 // Exercises ’ 264 // References 266 // 6 Entropie forces 267 // 6.1 Entropie continuum
models and mixtures 269 // 6.1.1 Random clothes-pins 269 // 6.1.2 The Asakura-Oosawa depletion interaction 273 // 6.1.3 Binary mixtures 277 // 6.2 Entropie lattice model: dimers 281 // 6.2.1 Basic enumeration 281 // 6.2.2 Breadth-first and depth-first enumeration 284 // 6.2.3 Pfaffian dimer enumerations 288 // 6.2.4 Monte Carlo algorithms for the monomer-dimer // problem 296 // 6.2.5 Monomer-dimer partition function 299 // Exercises 303 // References 305 // 7 Dynamic Monte Carlo methods // 307 // 7.1 Random sequential deposition 309 // 7.1.1 Faster-than-the-clock algorithms 310 // 7.2 Dynamic spin algorithms 313 // 7.2.1 Spin-flips and dice throws 314 // 7.2.2 Accelerated algorithms for discrete systems 317 // 7.2.3 Futility 319 // 7.3 Disks on the unit sphere 321 // 7.3.1 Simulated annealing 324 // 7.3.2 Asymptotic densities and paper-cutting 327 // 7.3.3 Polydisperse disks and the glass transition 330 // 7.3.4 Jamming and planar graphs 331 // Exercises 333 // References 335 // Acknowledgements 337 // Index 339

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