546
Subject Index
Bifurcation (cont.)
sequence, 75
tangent, 48
tree, 79
Billiard
circle
spectral statistics, 196
cut-circle, 221
D-billiard, 221
integrability, 221
laser, 223
Peres integrability test, 221
microwave experiment
Maxwell’s equations, 515
transverse electric modes, 518
transverse magnetic modes, 517
rectangular
microwave experiment, 197
spectral statistics, 196
ripple, 197, 215
Birkhoff coordinates, 215
Husimi distribution, 218
surface of section, 215
Sinai, 214, 229
energy level spacing, 214
3 -statistic, 215
3 -statistic, 196
stadium, 208
bouncing ball orbits, 209
microwave cavity, 209
microwave experiment, 197
scars, 197, 212
spectral statistics, 196, 209
3 -statistic, 211
whispering gallery orbits, 209
triangular, 196, 201
Birkhoff coordinates, 24, 198,
215, 230, 231, 263, 264, 269
ripple cavity, 270
Birkhoff’s fixed point theorem, 50, 53
Bloch momentum, 231, 232
Bloch states, 231
Bohr-Sommerfeld correspondence
principle, 235
Bohr-Sommerfeld quantization, 293
Bohr-Sommerfeld semiclassical
quantization, 318
Bose-Einstein distribution, 188, 192
Bounded quantum systems, 195
Branching tree, 122
Brillouin zone
soft Sinai lattice, 232
high symmetry points, 233
Brody distribution, 182, 211, 228
truncated, 350
C
Canonical transformation, 14, 400
Cantori, 80
noble, 80
Cantorus, 49
Caustics, 294
Center of mass, 529
Cesium atoms , 358
Chain rule, 310
Chaos, 12
classical, 48
definition, 36
Chaotic sea, 47, 49
Characteristic function, 519
Chirikov overlap criterion, 85, 345
Chirikov regime, 146
driven optical lattice, 384
Chi-squared confidence test, 196
Chlorine ion, 114
Circular ensembles, 493, 494
cluster functions, 508–510
COE, 493
CSE, 493
CUE, 493
information minimization, 494
probability density, 494
normalization constant, 494
polar form, 494
Circular Orthogonal Ensemble (COE)
relation to OE, 278
relation to OE , 279
Circular orthogonal ensemble (COE)
cluster functions, 508, 509
two-body cluster function, 511
Circular symplectic ensemble (CSE)
cluster functions, 509, 510
probability density, 507
two-body cluster function, 512
3 statistic, 512
equation for, 512
Circular unitary ensemble (CUE)
cluster functions, 508
3 -statistic
equation for, 510
Cluster expansion, 164
GU, 479
Cluster functions
relation between COE and OE, 249
Subject Index
Bifurcation (cont.)
sequence, 75
tangent, 48
tree, 79
Billiard
circle
spectral statistics, 196
cut-circle, 221
D-billiard, 221
integrability, 221
laser, 223
Peres integrability test, 221
microwave experiment
Maxwell’s equations, 515
transverse electric modes, 518
transverse magnetic modes, 517
rectangular
microwave experiment, 197
spectral statistics, 196
ripple, 197, 215
Birkhoff coordinates, 215
Husimi distribution, 218
surface of section, 215
Sinai, 214, 229
energy level spacing, 214
3 -statistic, 215
3 -statistic, 196
stadium, 208
bouncing ball orbits, 209
microwave cavity, 209
microwave experiment, 197
scars, 197, 212
spectral statistics, 196, 209
3 -statistic, 211
whispering gallery orbits, 209
triangular, 196, 201
Birkhoff coordinates, 24, 198,
215, 230, 231, 263, 264, 269
ripple cavity, 270
Birkhoff’s fixed point theorem, 50, 53
Bloch momentum, 231, 232
Bloch states, 231
Bohr-Sommerfeld correspondence
principle, 235
Bohr-Sommerfeld quantization, 293
Bohr-Sommerfeld semiclassical
quantization, 318
Bose-Einstein distribution, 188, 192
Bounded quantum systems, 195
Branching tree, 122
Brillouin zone
soft Sinai lattice, 232
high symmetry points, 233
Brody distribution, 182, 211, 228
truncated, 350
C
Canonical transformation, 14, 400
Cantori, 80
noble, 80
Cantorus, 49
Caustics, 294
Center of mass, 529
Cesium atoms , 358
Chain rule, 310
Chaos, 12
classical, 48
definition, 36
Chaotic sea, 47, 49
Characteristic function, 519
Chirikov overlap criterion, 85, 345
Chirikov regime, 146
driven optical lattice, 384
Chi-squared confidence test, 196
Chlorine ion, 114
Circular ensembles, 493, 494
cluster functions, 508–510
COE, 493
CSE, 493
CUE, 493
information minimization, 494
probability density, 494
normalization constant, 494
polar form, 494
Circular Orthogonal Ensemble (COE)
relation to OE, 278
relation to OE , 279
Circular orthogonal ensemble (COE)
cluster functions, 508, 509
two-body cluster function, 511
Circular symplectic ensemble (CSE)
cluster functions, 509, 510
probability density, 507
two-body cluster function, 512
3 statistic, 512
equation for, 512
Circular unitary ensemble (CUE)
cluster functions, 508
3 -statistic
equation for, 510
Cluster expansion, 164
GU, 479
Cluster functions
relation between COE and OE, 249