548
Subject Index
Eigenvector statistics, 183
Eigenvectors
Floquet (see Floquet eigenstates), 340
Eigenvector thermalization, 187
Elliptic functions, 88, 144, 407, 410, 416
Elliptic theta functions, 230
Energy Green’s function
1 DoF particle in potential well, 312
Energy level repulsion
molecules, 288
Energy surface, 28, 39
Ensembles
circular, 493
cluster functions, 510
Ergodicity
chaotic systems, 188
Euler gamma constant, 483
F
Fano resonance, 266
Fermi accelerator, 394
Fermi-Dirac distribution, 188, 192
Fermi’s golden rule
diamagnetic hydrogen, 331
Feynman path integrals, 294
Fibonacci numbers, 65, 68
Fixed points, 47–71
elliptic, 30, 47–113
dominant, 68
heteroclinic, 55, 56
homoclinic, 55, 56
hyperbolic, 30, 47–101
inversion, 55
regular, 55
inverse hyperbolic, 113
Floquet eigenstates, 342
delocalization, 340
driven optical lattice
entangle energy states, 382
Husimi function, 347
localization on resonances, 345
two primary resonance model, 346
Floquet eigenvalues
definition, 342
from time series, 350
nearest neighbor spacing, 350
Floquet energy
conservation
discrete time-translation invariance,
340
Floquet energy eigenvalues
level repulsion, 340
Floquet Hamiltonian, 344
eigenvalue equation, 344
Floquet map, 340, 343
delta-kicked rotor, 365
Floquet matrix, 341, 343, 350, 441
definition, 343
delta-kicked rotor, 367
driven optical lattice, 381
eigenstates, 343
eigenvalues, 343
STIRAP, 388
two primary resonance model, 347
Floquet scattering matrix, 394
Floquet states
driven optical lattice, 378
STIRAP, 387
Floquet theory, 340, 341
driven optical lattice, 378
Fundamental area, 104, 116
Fundamental constants
Gaussian units, 527
G
Galaxy, 22
Garton-Tomkins oscillations, 335
Gaussian
delta kicked, 103
Gaussian ensembles, 158, 467
probability density, 467
normalization constant, 467
Gaussian Orthogonal Ensemble (GOE),
155
eigenvalue statistics
nearest neighbor spacing, 178
scattering theory, 240
3 -statistic, 178
Gaussian potential, 229
Gaussian Symplectic Ensemble (GSE), 485
Gaussian Unitary Ensemble (GUE), 474
probability density, 474
3 -statistic, 482
Gaussian units, 525, 527
Generating functions, 14, 51
Generator
of infinitesimal transformation, 420
of rotation, 421
of space translation, 421
of time translation, 421
Golden mean, 64
inverse, 65
Green’s function
density of states, 295
energy, 307
free particle, 299
Subject Index
Eigenvector statistics, 183
Eigenvectors
Floquet (see Floquet eigenstates), 340
Eigenvector thermalization, 187
Elliptic functions, 88, 144, 407, 410, 416
Elliptic theta functions, 230
Energy Green’s function
1 DoF particle in potential well, 312
Energy level repulsion
molecules, 288
Energy surface, 28, 39
Ensembles
circular, 493
cluster functions, 510
Ergodicity
chaotic systems, 188
Euler gamma constant, 483
F
Fano resonance, 266
Fermi accelerator, 394
Fermi-Dirac distribution, 188, 192
Fermi’s golden rule
diamagnetic hydrogen, 331
Feynman path integrals, 294
Fibonacci numbers, 65, 68
Fixed points, 47–71
elliptic, 30, 47–113
dominant, 68
heteroclinic, 55, 56
homoclinic, 55, 56
hyperbolic, 30, 47–101
inversion, 55
regular, 55
inverse hyperbolic, 113
Floquet eigenstates, 342
delocalization, 340
driven optical lattice
entangle energy states, 382
Husimi function, 347
localization on resonances, 345
two primary resonance model, 346
Floquet eigenvalues
definition, 342
from time series, 350
nearest neighbor spacing, 350
Floquet energy
conservation
discrete time-translation invariance,
340
Floquet energy eigenvalues
level repulsion, 340
Floquet Hamiltonian, 344
eigenvalue equation, 344
Floquet map, 340, 343
delta-kicked rotor, 365
Floquet matrix, 341, 343, 350, 441
definition, 343
delta-kicked rotor, 367
driven optical lattice, 381
eigenstates, 343
eigenvalues, 343
STIRAP, 388
two primary resonance model, 347
Floquet scattering matrix, 394
Floquet states
driven optical lattice, 378
STIRAP, 387
Floquet theory, 340, 341
driven optical lattice, 378
Fundamental area, 104, 116
Fundamental constants
Gaussian units, 527
G
Galaxy, 22
Garton-Tomkins oscillations, 335
Gaussian
delta kicked, 103
Gaussian ensembles, 158, 467
probability density, 467
normalization constant, 467
Gaussian Orthogonal Ensemble (GOE),
155
eigenvalue statistics
nearest neighbor spacing, 178
scattering theory, 240
3 -statistic, 178
Gaussian potential, 229
Gaussian Symplectic Ensemble (GSE), 485
Gaussian Unitary Ensemble (GUE), 474
probability density, 474
3 -statistic, 482
Gaussian units, 525, 527
Generating functions, 14, 51
Generator
of infinitesimal transformation, 420
of rotation, 421
of space translation, 421
of time translation, 421
Golden mean, 64
inverse, 65
Green’s function
density of states, 295
energy, 307
free particle, 299