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Hans-Jürgen Stöckmann — Quantum Chaos: An Introduction

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Название: Quantum Chaos: An Introduction

Автор: Hans-Jürgen Stöckmann

Аннотация:

This volume provides a comprehensive and highly accessible introduction to quantum chaos. It emphasizes both the experimental and theoretical aspects of quantum chaos, and includes a discussion of supersymmetry techniques. Theoretical concepts are developed clearly and illustrated by numerous experimental or numerical examples. The author also shares the first-hand insights that he gleaned from his initiation of the microwave billiard experiments. Additional topics covered include the random matrix theory, systems with periodic time dependences, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book is an invaluable resource for graduate students and researchers working in quantum chaos.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2007

Количество страниц: 384

Добавлена в каталог: 21.10.2010

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Предметный указатель

$\Delta_{3}$ statistics      see “Spectral rigidity density of states”
$\Delta_{3}$ statistics, analytic bootstrap      318
$\Delta_{3}$ statistics, bouncing-ball contributions      293—295
$\Delta_{3}$ statistics, Gaussian ensembles      see “Gaussian ensembles averaged
$\Delta_{3}$ statistics, integrable systems      253—259
$\Delta_{3}$ statistics, oscillatory part      290—293 297 321
$\Delta_{3}$ statistics, semiclassical      see “Gutzwiller trace formula”
$\Delta_{3}$ statistics, smooth part      287—289 297
$\Delta_{3}$ statistics, vibrating blocks      24
$\Sigma^{2}$ statistics      see “Number variance”
action      248 264 272—275 282 292 297—301 304
Anderson model      166—169
Anisotropic Kepler problem      324
Anticommuting variables      122—126
Arithmetical groups      338
Artin’s billiard      see “Billiards Artin’s”
Atoms in magneto-optical traps      159—166
Autocorrelation function of propagating pulses      269—271
Autocorrelation function of scattering matrix elements      237—241
Autocorrelation function, spatial      233
Autocorrelation function, spectral      115 256 314
Avoided crossings      201—205
Berry — Robnik distribution      98—103
Berry’s phases      see “Geometrical phases”
BGS conjecture      see “Bohigas — Giannoni — Schmit conjecture”
Billiard experiments, antidot lattices      47—50
Billiard experiments, Josephson junctions      45—47
Billiard experiments, microwave cavities      27—45
Billiard experiments, quantum corrals      55—58
Billiard experiments, quantum dots      50—52
Billiard experiments, quantum wells      52—55
Billiard experiments, vibrating blocks      22—25
Billiard experiments, vibrating plates      15—19 25
Billiard experiments, water surface waves      19—22
Billiard experiments, water-filled cavities      25—27
Billiards with broken time-reversal symmetry      42—45 50—52 92—93 222—224
Billiards, Artin’s      338
Billiards, cardioid      99
Billiards, circular      17—18 20—21 27—28 50—51 55—57 99 213—215 243—244
Billiards, elbow-shaped      240 242
Billiards, hyperbola      117—118 310
Billiards, isospectral      37—39
Billiards, lemon      280—281
Billiards, non-Euclidean octagon      320—322 333—335 338
Billiards, pseudointegrable      17—18 32 38 98
Billiards, ray-splitting      36
Billiards, rectangular      17—18 23—24 34 46—47 50 67 98 222—224 253—258 311 314 333 336
Billiards, Robnik      98—103
Billiards, Sinai      17—18 23—25 40 48 50 88—91 196 200—201 202 222—224 227—229 236 290—291 298—299
Billiards, Sinai-stadium      25—26
Billiards, singular square      340—343
Billiards, stadium      7—8 17 20—22 27—28 31 35—36 37—38 45—46 50—51 57—58 90—91 197 202 218—219 230 234—235 238—239 242—244 269—271 275—276 280—281 285—286 293—295 297 305—306 311
Billiards, three-dimensional      36 40 90—91 227—229 235—236
Billiards, triangular      206 208—209
Bloch states      19—20 95—96 136 167 170
Bohigas — Giannoni — Schmit conjecture      88—92 169 214
Boosts      336
Bouncing-ball orbits      20—21 27—28 37—38 53—55 196 200—201 202 227—228 236 282 293—295 297
Break of time-reversal symmetry      see “Billiards with broken time-reversal symmetry”
Breit — Wigner formula      215—219 230 233 237
Brody distribution      93—94
Calogero — Moser system      186
Canonical equations      9 154 162 192 265 283—284
Cantori      11 145
Capillary waves      20
Caustic      269
Central limit theorem      146 232 240
Chladni figures      15—19
Circular ensembles      139—144 195 243
Conductance fluctuations      50—52 241—245 300—301 343
Conformal mapping technique      98 196 331
Conjugate-complex operator      68
Conjugated points      268—269 271 285
Correlated energy distribution      see “Gaussian ensembles correlated
Correlation hole      116—118 312
Coupled-channel Hamiltonians      219—224 245
Curvature distribution      200—203
Diabolic points      206
Diagonal approximation      257 315—317
Diffraction orbits      295
Diffusion in phase space, atoms in magneto-optical traps      163—166
Diffusion in phase space, dynamical localization      5 144—166 167
Diffusion in phase space, dynamical zeta function      319—325
Diffusion in phase space, Harper equation      181—182
Diffusion in phase space, hydrogen atoms in strong microwave field      156—159
Diffusion in phase space, standard map      11—13 145—150
Electron in a strong magnetic field      53—55 95—97 175—178 298—301
Encson fluctuations      237—241 242 343
Entropy barrier      321
Entropy, topological      see “Topological entropy”
Equations of motion      see “Canonical equations”
Excess      114—115
Exponential proliferation of periodic orbits      257 271 290—291 315 320—321 328
Feynman path integral      259—262
Fibonacci numbers      179—181
Floquet systems      11 60 88 136—139 141 146 158—159 165—166 167 187—188
Floquet theorem      136
Focal point      269
Form factor      see “Spectral form factor”
Gauss — Bonnet theorem      335 340
Gaussian curvature      330—331 335
Gaussian ensembles, averaged density of states      79—86 106—108 118—134
Gaussian ensembles, correlated energy distribution      77—79 194
Gaussian ensembles, correlated probability of matrix elements      73—77
Gaussian ensembles, definition      73—77
Genus of compact surfaces      335
Geometrical phases      205—209
Ghost orbits      295
Golden mean      179
Graded matrices      126—127
Graded trace      127
Grassmann variables      see “Anticommuting variables”
Gravity waves      22
Green function, non-Euclidean metrics      335—336
Green function, quantum mechanical      80—81 119—134 211 216—218 220—221 259—260
Green function, semiclassical      272—276 281—285 287—288 294 307—310
Gutzwiller trace formula      6 259—295 320 337
Hadamard prime number theorem      328
Hamilton — Jacobi equations      see “Canonical equations”
Hamilton’s principal function      see “Principal function”
Hardy — Littlewood conjecture      326
harmonic oscillator      41 104—107 253 258
Harper equation      174—182
Henon — Heiles potential      41
Hofstadter butterfly      177—179
Hubbard — Stratonovich transformation      126—130

Hydrogen atom in strong magnetic field      72—73 111—112 113—115 301—305
Hydrogen atom in strong microwave field      151—159
Information theory      75 193
Inside-outside duality      215
Instability exponent of orbits      278 327 338
Integrated density of states      see “Weyl formula”
Isospin      66
Kepler map      156
Kicked rotator      9—13 139 144—150 167 169
Kicked top      88 102 139 142
Kramer’s degeneracy      71
Lagrange differential equation      263
Lagrange function      262 263—265
Laplace — Beltrami operator      332
Lenz — Haake distribution      97—99
Level dynamics      36 40 183—209
Level spacing distribution      see “Nearest neighbour distance distribution”
Localization by destructive interference      19 37 94 167 169
Localization length      149—150 157—158 163 171 173—174
Localization, dynamical      see “Dynamical localization”
Localization, weak      see “Weak localization”
Magnetoresistance      48—49 50—51 241—245
Maslov index      252—253 285—286 292 297
Maxwell equations      27—29 43
Metric with constant negative curvature      see “Non-Euclidean metric”
Mobius transformation      331 336 341
Modular group      see “Billiards Artin’s”
Monodromy matrix      276—281 284 285 292 297
n-point correlation function      103—109 142 327
Nearest neighbour distance distribution from the integrable to the non-integrable regime      92—103 214—215
Nearest neighbour distance distribution, circular ensembles      142—144 214—215
Nearest neighbour distance distribution, coupled-channel Hamiltonian      222—224
Nearest neighbour distance distribution, Gaussian ensembles      31—33 63—65 86—92
Nearest neighbour distance distribution, Harper equation      178—182
Nearest neighbour distance distribution, integrable systems      67 255
Non-Euclidean billiards      338 339
Non-Euclidean metric      22 324 330—343
Nuclear data ensemble      63 111—112 113—115 117
Number variance      110—112 195 329 338
Orbit selection function      313
Orthogonal transformations      see “Transformations orthogonal”
Pascal’s limaQon      see “Billiards Robnik”
Pechukas — Yukawa model      184—195
Periodic orbits      36 37—38 55 111 196 256 275 282 285 290—291 294 296—343
Perturbing bead method      37 224—229
Poincare disk      331—338
Poincare half plane      339
Poincare section      9—10 99—100
Poisson distribution      31—32 67 92—103 143—144 180 194 214—215 255 258 339—340
Poisson sum relation      5—6 255—256
Porter — Thomas distribution      25—26 233—236
Principal function      262 264 272—273 293
Principle of uniformity      316
Probability density, quantum mechanical      259
Propagation in microwave billiards      7—9 40 271
Propagation of a wavepacket      3—6 269—271
Propagation on the Poincare disk      332—334
Propagator, quantum mechanical      259—262 270 293
Propagator, semiclassical      265—271 272 287 294
Pruning of orbits      290 324 328
Pseudo-orbits      323 328
Pseudosphere      331
Q factor      see “Quality factor”
Quality factor      23—24 27 34—35
Quantum mechanical localization      see “Dynamical localization”
Quantum mechanical probability density      see “Probability density quantum
Quantum mechanical propagator      see “Propagator quantum
Random superposition of plane waves      21—22 230—233
Replica trick      121—122 125
Riemann conjecture      325
Riemann curvature tensor      330
Riemann zeta function      322 325—330 338 342—343
Rigidity      see “Spectral rigidity”
Robnik billard      see “Billiards Robnik”
Rotator, kicked      see “Kicked rotator”
Saddle point integration      130—134 250
Scars      21—22 27—28 37—38 159 227—228 230 235 236 305—310 338
Scattering matrix      36 211—215 216 220—221
Selberg trace formula      330—338
Semicircle law      see “Wigner’s semi-circle law”
skewness      113—115
Skin depth      33
Sound figures      see “Chladni figures”
Spectral autocorrelation function      see “Autocorrelation function spectral”
Spectral form factor      115—118 257—259 311—319
Spectral rigidity      112—113 180—181 310—319 338 339
Spinor rotations      160 171 206
Standard map      9 145 156 163
Stationary phase approximation      250 255 258 263 266 272 282 287 325
Stirling’s formula      76 131
Sum rule of Hannay and Ozono de Almeida      314—317
Supersymmetry techniques      118—134 200 202 245
Symbolic dynamics      323—324 335
Symplectic transformations      see “Transformations symplectic”
Tight-binding systems      166—182
Time-evolution operator      137 140 207 259
Time-reversal operator      68
Time-reversal symmetry      69—73 140—144
Topological entropy      291 328
Tori, invariant      10—13 145 253 259
Trace formula, Gutzwiller      see “Gutzwiller trace formula”
Trace formula, Selberg      see “Selberg trace formula”
Transfer matrices      169—174 177
Transformations, orthogonal      69 141
Transformations, symplectic      72 141
Transformations, unitary      69 141
Two-level cluster function      see “Two-point correlation function”
Two-point correlation function      103—109 115 195 319 325—327
Unitary transformations      see “Transformations unitary”
Universal conductance fluctuations      see “Conductance fluctuations”
Universality classes      68—73
Wave functions, amplitude distributions      see “Porter — Thomas distribution”
Wave functions, bouncing-ball structures      see “Bouncing-ball orbits”
Wave functions, localized      see “Localization by destructive interference”
Wave functions, ridge structures      21—22 27—28 232
Wave functions, scarred      see “Scars”
Wave functions, spatial autocorrelation functions      see “Autocorrelation functions spatial”
wavepacket      see “Propagation of a wavepacket”
Weak localization      51 244—245
Weyl formula      24 34 288—289 290 294
Wigner distribution      33 63—65 66 87—91 92—103 143—144 205 214—215
Wigner function      309
Wigner’s semicircle law      85—86 108 142
WKB approximation      107 248 259
Yukawa conjecture      193—194 200—205
Zeta function, Riemann      see “Riemann zeta function”
“Can you hear the shape of the drum”      38

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