Ex Libris                        Wanted                           
blank

       
blank

blank
blank
blank
blank
Hans-Jürgen Stöckmann Quantum Chaos: An Introduction
Hans-Jürgen Stöckmann  Quantum Chaos: An Introduction









?
Ctrl+Enter


: Quantum Chaos: An Introduction

: Hans-Jürgen Stöckmann

:

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.


: en

: /

:

ed2k: ed2k stats

: 2007

: 384

: 21.10.2010

: | | ID
blank
$\Delta_{3}$ statistics      see Spectral rigidity density of states
$\Delta_{3}$ statistics, analytic bootstrap      318
$\Delta_{3}$ statistics, bouncing-ball contributions      293295
$\Delta_{3}$ statistics, Gaussian ensembles      see Gaussian ensembles averaged
$\Delta_{3}$ statistics, integrable systems      253259
$\Delta_{3}$ statistics, oscillatory part      290293 297 321
$\Delta_{3}$ statistics, semiclassical      see Gutzwiller trace formula
$\Delta_{3}$ statistics, smooth part      287289 297
$\Delta_{3}$ statistics, vibrating blocks      24
$\Sigma^{2}$ statistics      see Number variance
action      248 264 272275 282 292 297301 304
Anderson model      166169
Anisotropic Kepler problem      324
Anticommuting variables      122126
Arithmetical groups      338
Artins billiard      see Billiards Artins
Atoms in magneto-optical traps      159166
Autocorrelation function of propagating pulses      269271
Autocorrelation function of scattering matrix elements      237241
Autocorrelation function, spatial      233
Autocorrelation function, spectral      115 256 314
Avoided crossings      201205
Berry Robnik distribution      98103
Berrys phases      see Geometrical phases
BGS conjecture      see Bohigas Giannoni Schmit conjecture
Billiard experiments, antidot lattices      4750
Billiard experiments, Josephson junctions      4547
Billiard experiments, microwave cavities      2745
Billiard experiments, quantum corrals      5558
Billiard experiments, quantum dots      5052
Billiard experiments, quantum wells      5255
Billiard experiments, vibrating blocks      2225
Billiard experiments, vibrating plates      1519 25
Billiard experiments, water surface waves      1922
Billiard experiments, water-filled cavities      2527
Billiards with broken time-reversal symmetry      4245 5052 9293 222224
Billiards, Artins      338
Billiards, cardioid      99
Billiards, circular      1718 2021 2728 5051 5557 99 213215 243244
Billiards, elbow-shaped      240 242
Billiards, hyperbola      117118 310
Billiards, isospectral      3739
Billiards, lemon      280281
Billiards, non-Euclidean octagon      320322 333335 338
Billiards, pseudointegrable      1718 32 38 98
Billiards, ray-splitting      36
Billiards, rectangular      1718 2324 34 4647 50 67 98 222224 253258 311 314 333 336
Billiards, Robnik      98103
Billiards, Sinai      1718 2325 40 48 50 8891 196 200201 202 222224 227229 236 290291 298299
Billiards, Sinai-stadium      2526
Billiards, singular square      340343
Billiards, stadium      78 17 2022 2728 31 3536 3738 4546 5051 5758 9091 197 202 218219 230 234235 238239 242244 269271 275276 280281 285286 293295 297 305306 311
Billiards, three-dimensional      36 40 9091 227229 235236
Billiards, triangular      206 208209
Bloch states      1920 9596 136 167 170
Bohigas Giannoni Schmit conjecture      8892 169 214
Boosts      336
Bouncing-ball orbits      2021 2728 3738 5355 196 200201 202 227228 236 282 293295 297
Break of time-reversal symmetry      see Billiards with broken time-reversal symmetry
Breit Wigner formula      215219 230 233 237
Brody distribution      9394
Calogero Moser system      186
Canonical equations      9 154 162 192 265 283284
Cantori      11 145
Capillary waves      20
Caustic      269
Central limit theorem      146 232 240
Chladni figures      1519
Circular ensembles      139144 195 243
Conductance fluctuations      5052 241245 300301 343
Conformal mapping technique      98 196 331
Conjugate-complex operator      68
Conjugated points      268269 271 285
Correlated energy distribution      see Gaussian ensembles correlated
Correlation hole      116118 312
Coupled-channel Hamiltonians      219224 245
Curvature distribution      200203
Diabolic points      206
Diagonal approximation      257 315317
Diffraction orbits      295
Diffusion in phase space, atoms in magneto-optical traps      163166
Diffusion in phase space, dynamical localization      5 144166 167
Diffusion in phase space, dynamical zeta function      319325
Diffusion in phase space, Harper equation      181182
Diffusion in phase space, hydrogen atoms in strong microwave field      156159
Diffusion in phase space, standard map      1113 145150
Electron in a strong magnetic field      5355 9597 175178 298301
Encson fluctuations      237241 242 343
Entropy barrier      321
Entropy, topological      see Topological entropy
Equations of motion      see Canonical equations
Excess      114115
Exponential proliferation of periodic orbits      257 271 290291 315 320321 328
Feynman path integral      259262
Fibonacci numbers      179181
Floquet systems      11 60 88 136139 141 146 158159 165166 167 187188
Floquet theorem      136
Focal point      269
Form factor      see Spectral form factor
Gauss Bonnet theorem      335 340
Gaussian curvature      330331 335
Gaussian ensembles, averaged density of states      7986 106108 118134
Gaussian ensembles, correlated energy distribution      7779 194
Gaussian ensembles, correlated probability of matrix elements      7377
Gaussian ensembles, definition      7377
Genus of compact surfaces      335
Geometrical phases      205209
Ghost orbits      295
Golden mean      179
Graded matrices      126127
Graded trace      127
Grassmann variables      see Anticommuting variables
Gravity waves      22
Green function, non-Euclidean metrics      335336
Green function, quantum mechanical      8081 119134 211 216218 220221 259260
Green function, semiclassical      272276 281285 287288 294 307310
Gutzwiller trace formula      6 259295 320 337
Hadamard prime number theorem      328
Hamilton Jacobi equations      see Canonical equations
Hamiltons principal function      see Principal function
Hardy Littlewood conjecture      326
harmonic oscillator      41 104107 253 258
Harper equation      174182
Henon Heiles potential      41
Hofstadter butterfly      177179
Hubbard Stratonovich transformation      126130
Hydrogen atom in strong magnetic field      7273 111112 113115 301305
Hydrogen atom in strong microwave field      151159
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      913 139 144150 167 169
Kicked top      88 102 139 142
Kramers degeneracy      71
Lagrange differential equation      263
Lagrange function      262 263265
Laplace Beltrami operator      332
Lenz Haake distribution      9799
Level dynamics      36 40 183209
Level spacing distribution      see Nearest neighbour distance distribution
Localization by destructive interference      19 37 94 167 169
Localization length      149150 157158 163 171 173174
Localization, dynamical      see Dynamical localization
Localization, weak      see Weak localization
Magnetoresistance      4849 5051 241245
Maslov index      252253 285286 292 297
Maxwell equations      2729 43
Metric with constant negative curvature      see Non-Euclidean metric
Mobius transformation      331 336 341
Modular group      see Billiards Artins
Monodromy matrix      276281 284 285 292 297
n-point correlation function      103109 142 327
Nearest neighbour distance distribution from the integrable to the non-integrable regime      92103 214215
Nearest neighbour distance distribution, circular ensembles      142144 214215
Nearest neighbour distance distribution, coupled-channel Hamiltonian      222224
Nearest neighbour distance distribution, Gaussian ensembles      3133 6365 8692
Nearest neighbour distance distribution, Harper equation      178182
Nearest neighbour distance distribution, integrable systems      67 255
Non-Euclidean billiards      338 339
Non-Euclidean metric      22 324 330343
Nuclear data ensemble      63 111112 113115 117
Number variance      110112 195 329 338
Orbit selection function      313
Orthogonal transformations      see Transformations orthogonal
Pascals limaQon      see Billiards Robnik
Pechukas Yukawa model      184195
Periodic orbits      36 3738 55 111 196 256 275 282 285 290291 294 296343
Perturbing bead method      37 224229
Poincare disk      331338
Poincare half plane      339
Poincare section      910 99100
Poisson distribution      3132 67 92103 143144 180 194 214215 255 258 339340
Poisson sum relation      56 255256
Porter Thomas distribution      2526 233236
Principal function      262 264 272273 293
Principle of uniformity      316
Probability density, quantum mechanical      259
Propagation in microwave billiards      79 40 271
Propagation of a wavepacket      36 269271
Propagation on the Poincare disk      332334
Propagator, quantum mechanical      259262 270 293
Propagator, semiclassical      265271 272 287 294
Pruning of orbits      290 324 328
Pseudo-orbits      323 328
Pseudosphere      331
Q factor      see Quality factor
Quality factor      2324 27 3435
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      2122 230233
Replica trick      121122 125
Riemann conjecture      325
Riemann curvature tensor      330
Riemann zeta function      322 325330 338 342343
Rigidity      see Spectral rigidity
Robnik billard      see Billiards Robnik
Rotator, kicked      see Kicked rotator
Saddle point integration      130134 250
Scars      2122 2728 3738 159 227228 230 235 236 305310 338
Scattering matrix      36 211215 216 220221
Selberg trace formula      330338
Semicircle law      see Wigners semi-circle law
skewness      113115
Skin depth      33
Sound figures      see Chladni figures
Spectral autocorrelation function      see Autocorrelation function spectral
Spectral form factor      115118 257259 311319
Spectral rigidity      112113 180181 310319 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
Stirlings formula      76 131
Sum rule of Hannay and Ozono de Almeida      314317
Supersymmetry techniques      118134 200 202 245
Symbolic dynamics      323324 335
Symplectic transformations      see Transformations symplectic
Tight-binding systems      166182
Time-evolution operator      137 140 207 259
Time-reversal operator      68
Time-reversal symmetry      6973 140144
Topological entropy      291 328
Tori, invariant      1013 145 253 259
Trace formula, Gutzwiller      see Gutzwiller trace formula
Trace formula, Selberg      see Selberg trace formula
Transfer matrices      169174 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      103109 115 195 319 325327
Unitary transformations      see Transformations unitary
Universal conductance fluctuations      see Conductance fluctuations
Universality classes      6873
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      2122 2728 232
Wave functions, scarred      see Scars
Wave functions, spatial autocorrelation functions      see Autocorrelation functions spatial
wavepacket      see Propagation of a wavepacket
Weak localization      51 244245
Weyl formula      24 34 288289 290 294
Wigner distribution      33 6365 66 8791 92103 143144 205 214215
Wigner function      309
Wigners semicircle law      8586 108 142
WKB approximation      107 248 259
Yukawa conjecture      193194 200205
Zeta function, Riemann      see Riemann zeta function
Can you hear the shape of the drum      38
blank
blank
blank
HR
@Mail.ru
       © , 2004-2017
   | Valid HTML 4.01! | Valid CSS!