Quantum Signatures of Chaos
Springer 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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Time Reversal and Unitary Symmetries 15
Level Dynamics 141
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angular momentum antiunitary approximation asymptotic average behavior Berezinian block canonical transformations caustic chaotic Chap classical chaos classical limit cluster function coefficients constant contributions coordinates correlation function damping defined delta function density of levels determinant diagonal eigenstates eigenvalues eigenvectors ergodicity exponent exponential finite Floquet operator form factor Gaussian integral Grassmann Grassmannians Green function Hamiltonian Hermitian independent initial integrand integration variables kicked rotator kicked top Lagrangian manifold level density level dynamics level repulsion level spacing linear Lyapunov exponent Maslov Maslov index matrix elements Morse index motion orthogonal pairs particles periodic orbits perturbation phase space Phys Poisson brackets Poissonian propagator quantum mechanics quantum number quasi-energies random-matrix theory reader representation rescaling saddle-point Schrödinger equation Sect semicircle law semiclassical spacing distribution spectral fluctuations spectrum supermatrix symmetry symplectic time-reversal invariance trajectories two-point unitary unity vanishing vector yields zero