Quantum Signatures of ChaosSpringer Science & Business Media, 9 мар. 2013 г. - Всего страниц: 479 The warm reception of the first edition, as well as the tumultuous development of the field of quantum chaos have tempted me to rewrite this book and include some of the important progress made during the past decade. Now we know that quantum signatures of chaos are paralleled by wave signa tures. Whatever is undergoing wavy space-time variations, be it sound, electro magnetism, or quantum amplitudes, each shows exactly the same manifestations of chaos. The common origin is nonseparability of the pertinent wave equation; that latter "definition" of chaos, incidentally, also applies to classical mechanics if we see the Hamilton-Jacobi equation as the limiting case of a wave equation. At any rate, drums, concert halls, oscillating quartz blocks, microwave and opti cal oscillators, electrons moving ballistically or with impurity scattering through mesoscopic devices all provide evidence and data for wave or quantum chaos. All of these systems have deep analogies with billiards, much as the latter may have appeared of no more than academic interest only a decade ago. Of course, molec ular, atomic, and nuclear spectroscopy also remain witnesses of chaos, while the chromodynamic innards of nucleons are beginning to attract interest as methods of treatment become available. |
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1 | |
15 | 14 |
9 | 25 |
9 | 58 |
34 | 92 |
8 | 110 |
Level Clustering | 119 |
Periodic Orbits and the Semiclassical Density of Levels | 125 |
as TwoFreedom Autonomy | 289 |
8 | 303 |
Dissipative Systems | 323 |
5 | 329 |
5 | 339 |
Universality Classes of Level Repulsion | 354 |
9 | 356 |
Superanalysis for RandomMatrix Theory | 391 |
Level Density Fluctuations for Integrable Systems | 131 |
Level Dynamics | 140 |
9 | 163 |
Quantum Localization | 221 |
5 | 236 |
7 | 242 |
Semiclassical Roles for Classical Orbits | 250 |
78 | 436 |
in Matrix Space | 461 |
83 | 464 |
468 | |
475 | |
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Часто встречающиеся слова и выражения
angular momentum antiunitary approximation asymptotic average behavior Berezinian caustic chaotic classical chaos classical limit cluster function coefficients complex conjugate constant coordinates correlation function damping defined delta function density of levels determinant diagonal eigenstates eigenvalues eigenvectors energy surface equation ergodicity exponential finite Floquet operator form factor Gaussian integral global Grassmann Grassmannians Green function Hermitian independent initial integrand integration variables J₂ kicked rotator kicked top level density level dynamics level repulsion level spacing linear Maslov Maslov index matrix elements mean spacing Morse index motion N-torus orthogonal pairs particles periodic orbits perturbation phase space Poisson brackets Poissonian quantum number quasi-energies random random-matrix theory reader representation rescaling saddle-point Sect semicircle law semiclassical spacing distribution spectral fluctuations spectrum statistical supermatrix symmetry symplectic trace trajectories two-point unitary unity vanishing vector yields zero