Chaos and quantum physics
In the last decade the understanding of the relations between classical and quantum mechanics has advanced tremendously and the following broad themes are dealt with in this book:- bull; random matrices: a resurgence of an old theory brought in from nuclear physics, now the standard for analysing "signatures" of classical chaos in quantum systems; bull; the complex quantum behaviour of driven Hamiltonian systems and localization phenomena; bull; chaos in scattering systems and the properties of S -matrices; bull; spectra of quantum systems whose classical analogues are the geodesic flows on negatively curved compact manifolds; bull; the wealth of properties of wave functions for classically chaotic systems; bull; the rise and growth of the concept of chaos in all sectors of "physics of microscopic media": nuclear, atomic, molecular, solid-state physics.
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Models to study
Many degrees of freedom
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amplitude approximation asymptotic average behaviour billiard calculation chaos chaotic systems classical dynamics classical limit classical mechanics conjugate constant coordinate corresponding curve density diffusion discrete eigenfunctions eigenstates eigenvalues energy levels ensemble equation ergodic example exponential finite fixed point fluctuations Fourier transform frequency Gaussian geodesic Giannoni given Green's function Gutzwiller Hamiltonian systems hydrogen atom hyperbolic initial integral Lett level repulsion linear localization Lyapunov exponent M. V. Berry magnetic field manifold Math momentum nonlinear obtained oscillator parameter particle periodic orbits perturbation phase space Phys Physics plane Poincare Poisson potential problem properties quantization quantum chaos quantum mechanics quantum system regular resonance rotational scars scattering Selberg trace formula semiclassical limit sequence spacing distribution spectral spectrum stability stability matrix standard map statistical symmetry theory torus trace formula trajectory transition triangle unstable values variable Voros wave wavefunction wavepacket Wigner zero