550
Subject Index
Hydrogen(1-d)
microwave driven
fractional resonances, 376
resonance condition, 376
microwave driven resonances, 374
pendulum approximation, 375
I
Ideal coupling, 281
Infinite square well (classical)
time-periodically driven, 352
Infinite square-well (quantum)
eigenstates, 353
eigenvalues, 353
time-periodically driven, 353
Infinitesimal transformation, 420
generator, 420
rotation, 421
space translation, 421
time translation, 421
Information
extremization, 161, 477
loss, 196
minimization, 155, 157
Information extremization
Hermitian matrix, 163
unitary matrix, 276
Integrability
classical, 198
quantum, 196, 198
Peres test, 220
Integrable system, 12, 16
Integral of motion
isolating, 16, 30
non-isolating, 16
quantum, 198
Invariant measure, 431, 447
2×2 complex Hermitian matrix, 438
complex Hermitian matrix, 435, 437
definition, 432
GOE, 158
GSE, 485
GUE, 474
Hermitian matrices, 440
orthogonal matrix, 447
quaternion real matrix, 439, 440
real symmetric matrix, 433, 434
symmetric unitary matrix, 442
symplectic unitary matrix, 445
unitary matrix, 444, 446
volume, 447, 452, 453
Invariant metric
definition, 432
Involution, 75
Ionization
multi-photon, 340
J
Jacobian, 51, 276, 400, 438, 451, 477
Jacobian matrix, 319
Jupiter, 150
K
K-flows, 36, 40, 48, 56
KAM theorem, 137
KAM tori, 33, 59
action variables, 293
noble, 62
ripple cavity, 263
scaling behavior, 62
KAM torus, 48, 64, 126, 135, 139, 356
golden mean, 65, 88
inverse golden mean, 80
noble, 48, 65, 71, 83
Kepler orbit, 149
Kepler system, 13, 19, 95
anisotropic, 323
Kramer’s degeneracy, 428, 439
Kramers-Henneberger (KH) frame, 115
KS metric entropy, 36, 40, 56
Kummer’s equation, 531
L
Lagrange equations, 18, 398
Lagrange multipliers, 162
Lagrangian, 17, 52, 81, 398
Landau-Zener probability
avoided crossings , 391
Landauer conductance
ripple waveguide, 263
Lattice
Sinai
soft, 230
soft Sinai
band structure, 234
Brillouin zone, 232
Lattice surface of section (LSOS), 198,
230, 231
Level repulsion, 209, 241
Libration, 144
Linear operator
definition, 419
Lorentzian Orthogonal Ensemble (OE),
273, 277
relation to COE, 279
robust, 282
Subject Index
Hydrogen(1-d)
microwave driven
fractional resonances, 376
resonance condition, 376
microwave driven resonances, 374
pendulum approximation, 375
I
Ideal coupling, 281
Infinite square well (classical)
time-periodically driven, 352
Infinite square-well (quantum)
eigenstates, 353
eigenvalues, 353
time-periodically driven, 353
Infinitesimal transformation, 420
generator, 420
rotation, 421
space translation, 421
time translation, 421
Information
extremization, 161, 477
loss, 196
minimization, 155, 157
Information extremization
Hermitian matrix, 163
unitary matrix, 276
Integrability
classical, 198
quantum, 196, 198
Peres test, 220
Integrable system, 12, 16
Integral of motion
isolating, 16, 30
non-isolating, 16
quantum, 198
Invariant measure, 431, 447
2×2 complex Hermitian matrix, 438
complex Hermitian matrix, 435, 437
definition, 432
GOE, 158
GSE, 485
GUE, 474
Hermitian matrices, 440
orthogonal matrix, 447
quaternion real matrix, 439, 440
real symmetric matrix, 433, 434
symmetric unitary matrix, 442
symplectic unitary matrix, 445
unitary matrix, 444, 446
volume, 447, 452, 453
Invariant metric
definition, 432
Involution, 75
Ionization
multi-photon, 340
J
Jacobian, 51, 276, 400, 438, 451, 477
Jacobian matrix, 319
Jupiter, 150
K
K-flows, 36, 40, 48, 56
KAM theorem, 137
KAM tori, 33, 59
action variables, 293
noble, 62
ripple cavity, 263
scaling behavior, 62
KAM torus, 48, 64, 126, 135, 139, 356
golden mean, 65, 88
inverse golden mean, 80
noble, 48, 65, 71, 83
Kepler orbit, 149
Kepler system, 13, 19, 95
anisotropic, 323
Kramer’s degeneracy, 428, 439
Kramers-Henneberger (KH) frame, 115
KS metric entropy, 36, 40, 56
Kummer’s equation, 531
L
Lagrange equations, 18, 398
Lagrange multipliers, 162
Lagrangian, 17, 52, 81, 398
Landau-Zener probability
avoided crossings , 391
Landauer conductance
ripple waveguide, 263
Lattice
Sinai
soft, 230
soft Sinai
band structure, 234
Brillouin zone, 232
Lattice surface of section (LSOS), 198,
230, 231
Level repulsion, 209, 241
Libration, 144
Linear operator
definition, 419
Lorentzian Orthogonal Ensemble (OE),
273, 277
relation to COE, 279
robust, 282