Computational statistical physics: from billiards to Monte Carlo
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
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| Series: | Physics and astronomy online library
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 300 S. Ill., graph. Darst. |
| ISBN: | 3540421602 |
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MARC
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| 245 | 1 | 0 | |a Computational statistical physics |b from billiards to Monte Carlo |c Karl Heinz Hoffmann ; Michael Schreiber |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XV, 300 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics and astronomy online library | |
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| 650 | 7 | |a FÍSICA |2 larpcal | |
| 650 | 7 | |a MECÂNICA APLICADA |2 larpcal | |
| 650 | 7 | |a Statistische mechanica |2 gtt | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Statistical physics |x Data processing | |
| 650 | 4 | |a Statistical physics |x Methodology | |
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| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 2000 |z Chemnitz |2 gnd-content | |
| 689 | 0 | 0 | |a Statistische Physik |0 (DE-588)4057000-9 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hoffmann, Karl Heinz |e Sonstige |4 oth | |
| 700 | 1 | |a Schreiber, Michael |e Sonstige |4 oth | |
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Record in the Search Index
| _version_ | 1804128753592303616 |
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| adam_text | CONTENTS 1 GAME THEORY AND STATISTICAL MECHANICS ANDREAS ENGEL
..................................................... 1 1.1 INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 1 1.2 MATRIX GAMES . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 2 1.3 NASH EQUILIBRIA . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 BIMATRIX GAMES. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 9 1.5 WHAT ELSE? . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 14 2 CHAOTIC BILLIARDS
HANS J¨ URGEN KORSCH, FRANK ZIMMER .................................. 15
2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 15 2.2 BILLIARD SYSTEMS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 17 2.2.1 THE BILLIARD COMPUTER PROGRAM . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 18 2.3 INTEGRABLE SYSTEMS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 18 2.3.1 CIRCULAR BILLIARDS . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.2
ELLIPTICAL BILLIARDS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 20 2.4 *TYPICAL* BILLIARDS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 22 2.5 FURTHER COMPUTER EXPERIMENTS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 26 2.5.1 UNCERTAINTY AND
PREDICTABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 26 2.5.2 FINE STRUCTURE IN PHASE SPACE . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 28 2.6 GRAVITATIONAL BILLIARDS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29 2.7 QUANTUM BILLIARDS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 31 2.8 APPENDIXES . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 32 2.8.1 BILLIARD MAPPING . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.8.2
STABILITY MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 33 2.8.3 ELLIPTICAL BILLIARD: CONSTANT
OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . 34 REFERENCES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 35 3 COMBINATORIAL OPTIMIZATION
AND HIGH DIMENSIONAL BILLIARDS P´ AL RUJ´ AN
........................................................ 37 3.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 37 3.2 BILLIARDS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 40 3.3 LINEAR PROGRAMMING . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1 THE SIMPLEX ALGORITHM . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 43 3.3.2 THE INTERNAL POINT ALGORITHMS. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 VIII
CONTENTS 3.3.3 THE BILLIARD ALGORITHM I . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 45 3.3.4 THE BILLIARD ALGORITHM
II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45 3.3.5 DIFFICULT (INTEGER) LINEAR PROGRAMMING PROBLEMS . . . . . . . .
. . . . . . 46 3.4 THE BAYES PERCEPTRON. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4.1 THE
GEOMETRY OF PERCEPTRONS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 49 3.4.2 HOW TO PLAY BILLIARDS IN VERSION SPACE . . . . .
. . . . . . . . . . . . . . . . . . 51 3.5 BAYESIAN INFERENCE FOR THE
MIXTURE ASSIGNMENT PROBLEM . . . . . . . . . . . . . 53 3.6 CONCLUSION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 55 REFERENCES . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 55 4 THE STATISTICAL PHYSICS OF ENERGY LANDSCAPES: FROM SPIN
GLASSES TO OPTIMIZATION KARL HEINZ HOFFMANN
............................................... 57 4.1 AN INTRODUCTION
TO ENERGY LANDSCAPES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 57 4.2 THERMAL RELAXATION ON ENERGY LANDSCAPES . . . . . . . . . . .
. . . . . . . . . . . . . 58 4.2.1 MARKOV PROCESSES AND THE METROPOLIS
ALGORITHM . . . . . . . . . . . . . . . 58 4.2.2 COARSE-GRAINING
MOUNTAINOUS LANDSCAPES . . . . . . . . . . . . . . . . . . . . 60 4.2.3
COARSE GRAINING ON A COARSER SCALE . . . . . . . . . . . . . . . . . . .
. . . . . . . 64 4.2.4 TREE DYNAMICS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.5 A SERIOUS
APPLICATION: AGING EFFECTS IN SPIN GLASSES . . . . . . . . . . . 66 4.3
STOCHASTIC OPTIMIZATION: HOW TO FIND THE GLOBAL MINIMUM IN AN ENERGY
LANDSCAPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 68 4.3.1 SIMULATED ANNEALING . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.2 THRESHOLD
ACCEPTING AND TSALLIS ANNEALING . . . . . . . . . . . . . . . . . . . 70
4.3.3 ADAPTIVE SCHEDULES AND THE ENSEMBLE APPROACH . . . . . . . . . . .
. . . . 71 4.4 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 REFERENCES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 75 5 OPTIMIZATION OF PRODUCTION
LINES BY METHODS FROM STATISTICAL PHYSICS JOHANNES SCHNEIDER, INGO
MORGENSTERN ................................ 77 5.1 A SHORT OVERVIEW
OVER OPTIMIZATION ALGORITHMS . . . . . . . . . . . . . . . . . . . 77
5.2 METHODS FROM STATISTICAL PHYSICS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 79 5.3 A SIMPLE EXAMPLE: THE TRAVELING
SALESMAN PROBLEM . . . . . . . . . . . . . . . 80 5.4 OPTIMIZATION WITH
CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 83 5.5 THE LINEAR ASSEMBLY LINE PROBLEM . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 85 5.5.1 THE PROBLEM . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 85 5.5.2 THE MODEL . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5.3 COMPUTATIONAL
RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 87 5.6 THE NETWORK ASSEMBLY LINE PROBLEM . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 9 0 5.6.1 THE PROBLEM . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 9 0 5.6.2 THE MODEL . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 9 2 5.6.3
COMPUTATIONAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 9 3 5.7 CONCLUSION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 9 4 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 CONTENTS IX
6 PREDICTING AND GENERATING TIME SERIES BY NEURAL NETWORKS: AN
INVESTIGATION USING STATISTICAL PHYSICS WOLFGANG KINZEL
................................................... 97 6.1 INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 9 7 6.2 LEARNING FROM RANDOM SEQUENCES . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 8 6.3
GENERATING SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 100 6.4 PREDICTING TIME SERIES . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 103 6.5 PREDICTING WITH 100% ERROR . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 105 6.6 LEARNING FROM EACH
OTHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 107 6.7 COMPETING IN THE MINORITY GAME . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 108 6.8 PREDICTING HUMAN
BEINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 109 6.9SUMMARY . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 111 7 STATISTICAL
PHYSICS OF CELLULAR AUTOMATA MODELS FOR TRAFFIC FLOW MICHAEL
SCHRECKENBERG, ROBERT BARLOVI´ C, WOLFGANG KNOSPE, HUBERT KL¨ UPFEL
.................................................... 113 7.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 113 7.2 BASIC MEASUREMENTS OF
TRAFFIC FLOW SIMULATIONS WITH CA MODELS . . . . . 114 7.3 FUNDAMENTALS
OF THE NASCH MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 115 7.4 THE VDR MODEL . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.5 MODEL WITH
ANTICIPATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 121 7.6 DISCUSSION AND CONCLUSION . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.7
APPENDIX: SIMULATING PEDESTRIAN DYNAMICS AND EVACUATION PROCESSES 124
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 126 8 SELF-ORGANIZED
CRITICALITY IN FOREST-FIRE MODELS KLAUS SCHENK, BARBARA DROSSEL, FRANZ
SCHWABL ......................... 127 8.1 INTRODUCTION . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 127 8.2 THE SPIRAL STATE AND THE SOC STATE . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 128 8.2.1 PROPERTIES OF THE
SOC STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 128 8.3 FFM WITH THE TREE DENSITY AS PARAMETER . . . . . . . . . . .
. . . . . . . . . . . . . . 131 8.3.1 REMOVAL OF TREE CLUSTERS . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.3.2
ONE-BY-ONE REMOVAL OF TREES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 132 8.4 CONCLUSION . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8.5 APPENDIXES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 133 8.5.1 EXACT RESULTS IN
ONE DIMENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
133 8.5.2 MEAN FIELD THEORY . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 136 8.5.3 IMMUNITY . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 138 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 X
CONTENTS 9 NONLINEAR DYNAMICS OF ACTIVE BROWNIAN PARTICLES WERNER
EBELING .................................................... 141 9.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 141 9.2 EQUATIONS OF MOTION,
FRICTION AND FORCES . . . . . . . . . . . . . . . . . . . . . . . . . .
142 9.3 TWO-DIMENSIONAL DYNAMICS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 144 9.4 CONCLUSION . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 150 REFERENCES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 10
FINANCIAL TIME SERIES AND STATISTICAL MECHANICS MARCEL AUSLOOS
.................................................... 153 10.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 153 10.2 PHASE, AMPLITUDE AND
FREQUENCY REVISITED . . . . . . . . . . . . . . . . . . . . . . . 155
10.2.1 COHERENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 155 10.2.2 ROUGHNESS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 155 10.2.3 PERSISTENCE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 156 10.3 POWER LAW
EXPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 156 10.3.1 PERSISTENCE AND SPECTRAL DENSITY . . .
. . . . . . . . . . . . . . . . . . . . . . . . 156 10.3.2 ROUGHNESS,
FRACTAL DIMENSION, HURST EXPONENT, AND DETRENDED FLUCTUATION ANALYSIS .
. . . . . . . . . . . . . . . . . . . . . . . . 159 10.4 CONCLUSION . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 162 10.5 APPENDIXES . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 164 10.5.1 MOVING AVERAGES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 164 10.5.2 DISCRETE SCALE
INVARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 164 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 11 *GO
WITH THE WINNERS* SIMULATIONS PETER GRASSBERGER AND WALTER NADLER
................................. 169 11.1 INTRODUCTION . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 169 11.2 AN EXAMPLE: A LAMB IN FRONT OF A PRIDE OF LIONS . .
. . . . . . . . . . . . . . . . 170 11.3 OTHER EXAMPLES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 173 11.3.1 MULTIPLE SPANNING PERCOLATION CLUSTERS . . . . . . . .
. . . . . . . . . . . . . 173 11.3.2 POLYMERS . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
11.3.3 LATTICE ANIMALS (RANDOMLY BRANCHED POLYMERS) . . . . . . . . . .
. . 180 11.4 IMPLEMENTATION DETAILS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 181 11.4.1 DEPTH FIRST
VERSUS BREADTH FIRST . . . . . . . . . . . . . . . . . . . . . . . . . .
182 11.4.2 CHOOSING W . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 183 11.4.3 CHOOSING THE BIAS . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
183 11.4.4 ERROR ESTIMATES AND RELIABILITY TESTS. . . . . . . . . . . .
. . . . . . . . . . . 185 11.5 DIFFUSION QUANTUM MONTE CARLO . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 187 11.6
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 188 REFERENCES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 189 CONTENTS XI 12 APERIODICITY AND DISORDER *
DO THEY PLAY A ROLE? UWE GRIMM
....................................................... 191 12.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 19 1 12.2 THE ISING MODEL . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 19 3 12.2.1 THE SQUARE-LATTICE ISING MODEL . . . . . . .
. . . . . . . . . . . . . . . . . . . . 19 3 12.2.2 PHASE TRANSITIONS
AND CRITICAL EXPONENTS . . . . . . . . . . . . . . . . . . . 19 4 12.2.3
THE ISING-MODEL PHASE TRANSITION . . . . . . . . . . . . . . . . . . . .
. . . . . 19 6 12.2.4 THE ISING QUANTUM CHAIN . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 19 7 12.2.5 EFFECTS OF DISORDER:
SOME GENERAL REMARKS . . . . . . . . . . . . . . . . . 19 7 12.3
HEURISTIC SCALING ARGUMENTS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 19 8 12.4 RANDOM ISING MODELS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
200 12.5 APERIODIC ISING MODELS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 201 12.5.1 APERIODIC TILINGS
ON THE COMPUTER . . . . . . . . . . . . . . . . . . . . . . . . 201
12.5.2 ISING MODELS ON PLANAR APERIODIC GRAPHS . . . . . . . . . . . . .
. . . . . . 204 12.5.3 APERIODIC ISING QUANTUM CHAINS . . . . . . . . .
. . . . . . . . . . . . . . . . . 207 12.6 SUMMARY AND CONCLUSIONS . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
208 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 209 13 QUANTUM
PHASE TRANSITIONS THOMAS VOJTA
..................................................... 211 13.1
INTRODUCTION: FROM THE MELTING OF ICE TO QUANTUM CRITICALITY . . . . . .
. 211 13.2 BASIC CONCEPTS OF PHASE TRANSITIONS AND CRITICAL BEHAVIOR . .
. . . . . . . . 214 13.3 HOW IMPORTANT IS QUANTUM MECHANICS? . . . . . .
. . . . . . . . . . . . . . . . . . . . 217 13.4 QUANTUM CRITICAL POINTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 220 13.5 EXAMPLE: TRANSVERSE FIELD ISING MODEL . . . . . . . . .
. . . . . . . . . . . . . . . . . . 221 13.6 QUANTUM PHASE TRANSITIONS
AND NON-FERMI LIQUIDS . . . . . . . . . . . . . . . . 224 13.7 SUMMARY
AND OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 226 REFERENCES . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 226 14 INTRODUCTION TO ENERGY LEVEL STATISTICS BERNHARD KRAMER
.................................................. 227 14.1 INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 227 14.2 STATISTICS OF ENERGY LEVELS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
14.3 LEVEL SPACING DISTRIBUTION . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 230 14.4 LEVEL REPULSION AND
SYMMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 231 14.5 GAUSSIAN ENSEMBLES. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 233 14.6 LEVEL SPACING
DISTRIBUTION AT THE ANDERSON TRANSITION . . . . . . . . . . . . . 236
14.7 FLUCTUATIONS OF ENERGY LEVELS OF QUANTUM DOTS . . . . . . . . . . .
. . . . . . . . 238 14.8 CONCLUSION . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 239 XII CONTENTS 15
RANDOMNESS IN OPTICAL SPECTRA OF SEMICONDUCTOR NANOSTRUCTURES ERICH
RUNGE ....................................................... 241 15.1
SPECTRA OF SEMICONDUCTOR NANOSTRUCTURES . . . . . . . . . . . . . . . .
. . . . . . . . . 241 15.2 ANDERSON MODEL, WAVEFUNCTION LOCALIZATION,
AND MOBILITY EDGE . . . . . 243 15.3 REMARKS ON MACROSCOPIC SPECTRA . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 15.4
REPULSION OF ENERGY LEVELS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 248 15.5 MICROSCOPIC RELAXATION KINETICS . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 15.6
RADIATIVE-LIFETIME DISTRIBUTION . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 251 15.7 RAYLEIGH SCATTERING, SPECKLES, AND
ENHANCED BACK-SCATTERING . . . . . . . 252 15.8 SUMMARY . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 255 REFERENCES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
256 16 CHARACTERIZATION OF THE METAL*INSULATOR TRANSITION IN THE
ANDERSON MODEL OF LOCALIZATION MICHAEL SCHREIBER, FRANK MILDE
...................................... 259 16.1 THE METAL*INSULATOR
TRANSITION IN DISORDERED SYSTEMS . . . . . . . . . . . . . 259 16.2 THE
TRANSFER MATRIX METHOD . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 262 16.3 MULTIFRACTAL ANALYSIS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
16.4 ENERGY LEVEL STATISTICS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 272 REFERENCES . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 277 17 PERCOLATION, RENORMALIZATION AND QUANTUM HALL
TRANSITION RUDOLF A. R¨ OMER
.................................................. 279 17.1 INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 279 17.2 PERCOLATION . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 280 17.2.1 THE PHYSICS OF CONNECTIVITY . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 280 17.2.2 THE COLORING ALGORITHM . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
17.2.3 THE GROWTH ALGORITHM . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 283 17.2.4 THE FRONTIER ALGORITHM . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 17.3
REAL-SPACE RENORMALIZATION . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 285 17.3.1 MAKING USE OF SELF-SIMILARITY. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 17.3.2 MONTE
CARLO RG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 286 17.4 THE QUANTUM HALL EFFECT . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 17.4.1
BASICS OF THE IQHE . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 287 17.4.2 RG FOR THE CHALKER*CODDINGTON NETWORK
MODEL . . . . . . . . . . . . . 289 17.4.3 CONDUCTANCE DISTRIBUTIONS AT
THE QH TRANSITION . . . . . . . . . . . . . 29 1 17.5 SUMMARY AND
CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 29 3 REFERENCES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29 3 INDEX ............................................................
295
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| indexdate | 2024-07-09T18:54:15Z |
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| spelling | Computational statistical physics from billiards to Monte Carlo Karl Heinz Hoffmann ; Michael Schreiber Berlin [u.a.] Springer 2002 XV, 300 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library ESTATÍSTICA larpcal Fysische informatica gtt FÍSICA larpcal MECÂNICA APLICADA larpcal Statistische mechanica gtt Datenverarbeitung Statistical physics Data processing Statistical physics Methodology Statistische Physik (DE-588)4057000-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2000 Chemnitz gnd-content Statistische Physik (DE-588)4057000-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Hoffmann, Karl Heinz Sonstige oth Schreiber, Michael Sonstige oth SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009517964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Computational statistical physics from billiards to Monte Carlo ESTATÍSTICA larpcal Fysische informatica gtt FÍSICA larpcal MECÂNICA APLICADA larpcal Statistische mechanica gtt Datenverarbeitung Statistical physics Data processing Statistical physics Methodology Statistische Physik (DE-588)4057000-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4128130-5 (DE-588)1071861417 |
| title | Computational statistical physics from billiards to Monte Carlo |
| title_auth | Computational statistical physics from billiards to Monte Carlo |
| title_exact_search | Computational statistical physics from billiards to Monte Carlo |
| title_full | Computational statistical physics from billiards to Monte Carlo Karl Heinz Hoffmann ; Michael Schreiber |
| title_fullStr | Computational statistical physics from billiards to Monte Carlo Karl Heinz Hoffmann ; Michael Schreiber |
| title_full_unstemmed | Computational statistical physics from billiards to Monte Carlo Karl Heinz Hoffmann ; Michael Schreiber |
| title_short | Computational statistical physics |
| title_sort | computational statistical physics from billiards to monte carlo |
| title_sub | from billiards to Monte Carlo |
| topic | ESTATÍSTICA larpcal Fysische informatica gtt FÍSICA larpcal MECÂNICA APLICADA larpcal Statistische mechanica gtt Datenverarbeitung Statistical physics Data processing Statistical physics Methodology Statistische Physik (DE-588)4057000-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | ESTATÍSTICA Fysische informatica FÍSICA MECÂNICA APLICADA Statistische mechanica Datenverarbeitung Statistical physics Data processing Statistical physics Methodology Statistische Physik Numerisches Verfahren Konferenzschrift 2000 Chemnitz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009517964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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