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| Haake F. — Quantum signatures of chaos |
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| Предметный указатель |
Accelerated decoherence 329 331—334
Action and angle variables 120
Adiabatic invariance 215 218
Anderson model 223 225 442
Antidot structures 320
Antilinearity 16 35 357
Antiunitarity 16 17 35 356
Antiunitary symmetries 3 15—36 356 367 369
Asymptotic level spacing distributions 69—78
Avoided crossing 38 39 156
Baker map 258 292 321
Band matrices 221 224 442—458
BBGKY hierarchy 210
Berezinian 81 410 427 431
Berry conjecture 63 189
Berry — Robnik conjecture 317
Berry's diabolo 45
Bifurcation 318
Billiard 63 182 188
Billiard on surface of negative curvature 160
Bloch functions 223
Bloch vector 386
Bohigas — Giannoni — Schmit conjecture 8 47 142
Bootstrap 304—311 316
Born approximation 325 377 390
Bose — Einstein condensate 2 320
Break time 8 9 228 236 380 382
Brownian motion 9 142 198 218
Calogero — Moser dynamics 146
canonical ensemble 163 175
Canonical transformations of Hamiltonians or Floquet operators 19 31 37
Canonical transformations, orthogonal 20 26 32
Canonical transformations, symplectic 25 33
Canonical transformations, unitary 19 23 32
Cat map 160 265 274
Caustic 120 261 275 281 321
Caustic, g-space 121 279
Caustic, p-space 121 279
Central limit theorem 86 312
Chaotic resonator 320
Chapman — Kolmogorov equation 200
Chirikov's standard map 227 374
Circular ensembles of random matrices 68 175 333 389
Cluster function 67 83 84 91—95 112 118 139 210
Codimension of a level crossing 40 43 53 68 123 148 156 161 317
Coherence 329
Coherent states 329 388
Coherent states of an angular momentum 239 388
Collapse and revival 2 11 245
Collision time 190
Complex (quasi) energy 10 68 323 339—346
Complex conjugation of Grassmannians 400 406 421 458
Conductance 179
Conjugate points 260 277
Conventional time reversal 17 25
Coulomb gas model 203 209—215 218
Coupling agents 325
Covariance under time reversal of Floquet operators 31
Cubic repulsion 343 357 367 369
Cumulants 93 94 98
Cycle expansion 319
Damped rotator 374—382
Degree of level repulsion 5 11 34 40 42
Delta function of a Grassmann variable 438
Density-density correlation function 66 68 133 136
Detailed balance 204 369—374
Determinants as Gaussian integrals 78—82 186 347
Diagonal approximation 294
Differential forms 362
Diffusion 8 199 221 227 376 380
Disordered systems 35 223 234 392 442
Dyadic vector 332 334
Dyson — Pastur equation 211
Ehrenfest time 87 274 296 318
Eigenvector distributions 60
Emstein — Brillouin — Keller approximation 121 152
Energy-dependent propagator 267
Equilibration of spectra 190 207
Ergodicity 87 120 157
Ergodicity of level dynamics 156
Ergodicity of random-matrix ensembles 47 64 95 102 175 199
Euler — Maclaurin summation formula 355
Exponential proliferation 257 274 293 313
Fermi's golden rule 328 331 387
Fictitious-particle dynamics 9 144 146 176 191
Floquet operator 8 10 11 27 30 31 63 142 226
Flow 15
Fluctuation-dissipation theorem 326
Focal points 261
Fokker — Planck equation 201 202 209
Form factor 83 85 90 92 102 114
Fresnel integral 82 254
Frobenius — Perron operator 319
Functional equation 100 274 305
Furstenberg's theorem 224 228
Gap probability 71 124 163 193
Gaussian ensembles of random matrices 47 67 176 179 202 218 344 346 356
Gaussian integral, multiple 78 233 249 347
Ghost orbits 318
Ginibre's ensemble 346
graphs 274
Grassmann variables 78 347 389
Grassmann variables, complex conjugation of 393 404 406
Green function 58 182 232 392 416 417 441
Green function, advanced 424
Green function, retarded 424
Gross — Pitaevski equation 2 320
Group, SO(n) 20
Group, SU(n) 19
Group, symplectic 25
Hamilton — Cayley theorem 98 267 274
Hamilton — Jacobi equation 2 44
Hamiltonian embedding of dissipative dynamics 323
Hard modes 427 449
Hartwig — Fischer theorem 104
Heat bath 323 377 387
Heisenberg time 87 92 295 297 304 310 318
HOdA sum rule 292—295 298 301 315 316
Hole probability 352—356
Hubbard — Stratonovich transformation 394 407 414 442
Hydrogen 26 320
Inverse participation ratio 444
Jacobi equation 260
Jacobian for Grassmann variables see “Berezinian”
Joint distribution of eigenvalues of Gaussian ensembles 51 54 346
Kepler problem 364
Kick 28
Kicked rotator 7—9 11 29 31 221 374 392
Kicked rotator vs Anderson model 225
Kicked rotator, experiment 222
Kicked rotator, limit of top 247
Kicked top 2—5 11 29 31 33 38 63 112 195 222 237 246 341 386
Kicked top, classical phase space of 152
Kicked top, damped 340
Kramers' degeneracy 3 5 21 32 40 45 50 83 91 156
Lagrangian manifold 251 275—280 321
Lagrangian manifold in the energy shell 277
Langevin equation 375
Lax form 147 217 218
Legendre transformation 268
Level clustering 3 11 59 119 223
Level crossing 123
Level crossing, intermultiplet 148
Level crossing, intramultiplet 149
Level curvature 179—187
Level equilibration 190 195
Level repulsion 3 9 11 37 59 221 223
| Level repulsion, complex levels 341
Level spacing distribution, complex levels 352
Level staircase 59
Level velocity 187—190
Level width 10 11 370
Liouville — Von Neumann equation 324
Lloyd's model 223 231 444
Local and global energy scales 58 207—215
localization 221—248 392 442—458
Localization length 10 11 117 157 159 221 223 231 236 443 444
Localization, destruction of 323 374 380
Lyapunov exponent 1 6 225 256 293 296
MAP 27
Map, embedding in flow 289
Markovian processes 200 323 325 377 390
Maslov index 121 264 289
Master equation 10 323—331 377 383 387
Micro canonical ensemble 148 160 162 163
Microreversibility 369
Microwave resonators 179
Minimality vs extremality of the action 258
Mixed phase space 274 317—320
Moment-generating function 407
Monodromy matrix 264 285 293 300 307
Morse index 255—258 260 264 268 284
Morse theorem 260
Multiplet 37 123 141 148
Nearly degenerate perturbation theory 38 156 367
Neben-diagonal 383
Newton's formulae 98 263 267 304
Nilpotent 400 406 411 421
Noether's theorem 362
Nonconventional time reversal 25 34 35
Nonseparability 2 44
Normal form 318
Normal form, codimension of 318
Numerical variable 400 403 405 406 421
Ornstein — Uhlenbeck process 201
Overdamped pendulum 328
Parisi — Sourlas — Efetov — Wegner theorem 412 429 441
path integral 253
Pauli master equation 327 378
Pauli matrices 18 24
Pechukas — Yukawa gas 9 148 175 218 360
Pechukas — Yukawa gas, confined 176
Periodic orbits 64 117 119 126 160
Periodically kicked systems 31
Pfaffian 80 89 204
Planck cell 241 317 320
Poincare map 275
Poisson brackets 15 119 145 146 217 239 361 365
Poisson brackets from commutators 152
Poisson summation formula 126 132 193
Poissonian ensemble 207
Poissonian process 3 5 11 123 139 344 345 388
Pollicott — Ruelle resonances 319
Porter — Thomas distribution 63
Primitive periodic orbit 263
Pseudo-orbit 308
Pseudo-vector 26
Quantum chaos criterion 44 63 323
Quantum map 28 83 224 226 228 332 339 350 356 379
Quantum measurement process 331
Quantum well 320
Quasi-energy 3 28;
Quasi-periodicity 1 225 236 242 244 323 336
Quaternion real matrices 24 25 51
Rabi frequency 386
Random potential see “Disordered systems”
Random unitary matrices 47
Random-phase approximation 226 236 249 375
Rate equation 327 372 378
Recurrence 1 2 12 242 245 331
Replica trick 234
Resummation of periodic orbits 274
Riemann zeta function 78
Riemann — Siegel look-alike 305 310
Rydberg states 27
Saddle-point integration 396
Scars 64 319
Schrodinger cat state 10 329
Schrodinger cat state, long-lived 330
Second variation 254 416 427
Secular coefficients 98 106 116
Self-averaging 43 157 191 317 333 334
Self-correlation terms 266
Self-inversiveness 100 267 304
Semi-Poissonian distribution 139
Semicircle law 57 60 66 117 181 202 208 399 442
Semiclassical limit 119—138 251—320 384
Semiclassical quantization 311
Sensitivity to initial data 3
Sensitivity to initial data to perturbations 3 228 245
Sigma model 391 422
Sigma model, one-dimensional 442—458
skewness 383
Soft modes 427
Sparse matrices 441
Spectral determinant see “Secular polynomial”
Spin relaxation 325
Stability matrix see “Monodromy matrix”
Stable manifold 279
Stationary-phase approximation 128 129 132 254
Strange Attractor 333 335 375
Stroboscopic description 8 28
Super-radiance master equation 386
Superfluorescence 326
Superintegral 393
Supermatrix 401
Superposition of spectra 124 345 346
Supertrace 401
Supervector 400
Sutherland — Moser dynamics 146
Symmetry breaking 198—207
Taylor series for level spacing distributions 77
Tetrad 358
Thomas — Fermi distribution 126 130 131 139 273
Thouless formula 233
Thouless time 443
Threefold way 35
Time ordering 27 30
Time reversal 15—36
Time-scale separation 208—215 221 323 325 329
Toeplitz determinant 85 103 104
Torus quantization 7 121
Transition from clustering to repulsion 142 219 318
Transitions between universality classes 9 142 206—215 218
Trotter's product formula 252
Truncated exponential 352
Turning point 268
Two-body collisions 155
Unfolding inhomogeneous spectra 60 131 137 213 340 342
Universality of spectral fluctuations 9 37 47 142
Vandermonde determinant 69 88 101 205 347
von Neumann — Wigner theorem 38
Wave chaos 2 44 320
Wedge product 406 434
Weyl's law 58 126 131 159 272—274
Wick's theorem 407 447 459
Wick's theorem for Grassmann variables 409
Wick's theorem, superanalytic 410
Wigner distributions 54 59 69 117
Wigner function, Husimi function 319 306 320
WKB 152 281
Wojciechowski dynamics 146
Zaslavsky's map 374 379 381
Zeta function 300 305
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