Stochasticity and Quantum Chaos: Proceedings of the 3rd Max Born Symposium, Sobótka Castle, September 15-17, 1993

ISBN-13: 9789401040761 / Angielski / Miękka / 2012 / 226 str.

Zbigniew Haba;Wojciech Cegla;Lech Jakobczyk

Opis

This volume covers a wide range of problems in the quantum mechanics of non-integrable systems presented by experts in the field. The main part of the work concerns quantum chaos, and dynamical aspects of chaos in particular. Among the subjects which are treated are: periodic perturbations, small denominators in quantum mechanics, tunneling in the presence of a periodic perturbation, chaotic scattering, quantum maps, level statistics of chaotic systems and random matrices. The papers are concerned with mathematically rigorous derivations of results, as well as with their physical applications, such as scattering, ionization and tunneling. The papers discuss recent results which have not been published in book form before. All contributors present new methods to approach quantum chaos rather than extending conventional techniques. This book will be of interest to specialists in the field of dynamical systems, quantum mechanics and stochastic processes. It can also serve as an outstanding introduction to graduate and postgraduate students of theoretical physics and mathematics.

Spis treści

Foreword. The quantal fattening of fractals; N.L. Balazs. How and when quantum phenomena become real; Ph. Blanchard, A. Jadczyk. Chaotic dynamics in a periodically driven anharmonic oscillator; Yu.L. Bolotin, V.Yu. Gonchar, M.Ya. Granovsky. Coherent and incoherent dynamics in a periodically driven bistable system; T. Dittrich, F. Grossman, P. Hänggi, B. Oelschlägel, R. Utermann. The Ehrenfest theorem for Markov diffusions; P. Garbaczewski. The quantum state diffusion model, asymptotic solutions, thermal equilibrium and Heisenberg picture; N. Gisin. Stochastic representation of quantum dynamics; Z. Haba. Level repulsion and exceptional points; W.D. Heiss, W.-H. Steeb. Type-II intermittency in the presence of additive and multiplicative noise; H. Herzel, F. Argoul, A. Arneodo. Aspects of Liouville integrability in quantum mechanics; J. Hietarinta. KAM techniques for time dependent quantum systems; H.R. Jauslin. Dissipation and noise in quantum mechanics; N.G. van Kampen. Irregular scattering, number theory, and statistical mechanics; A. Knauf. Band random matrices, kicked rotator and disordered systems; L. Molinari. Robust scarred states; D. Richards. The quasiclassical statistical description of quantum dynamical systems and quantum chaos; Yu.P. Virchenko. Quantum measurement by quantum brain; M. Jibu, K. Yasue. Time reversal and Gaussian measures in quantum physics; J.C. Zambrini. Stochastic resonance in bistable systems with fluctuating barriers; L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, S. Santucci. Index.