Stochasticity and Quantum Chaos

These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) as a nrst volume of a complete monograph (supposedly to be written by another person). His lectures concern the quantum mechanics of integrable systems. The quantum mechanics of non-integrable systems was the subject of the Third Max Born Symposium. It is known that classical non-integrable Hamiltonian systems show a chaotic behaviour. On the other hand quantum systems bounded in space are quasiperi odic. We believe that quantum systems have a reasonable classical limit. It is not clear how to reconcile the seemingly regular behaviour of quantum systems with the possible chaotic properties of their classical counterparts. The quantum proper ties of classically chaotic systems constitute the main subject of these Proceedings. Other topics discussed are: the quantum mechanics of dissipative systems, quantum measurement theory, the role of noise in classical and quantum systems.

Texte du rabat

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.

Contenu
The quantal fattening of fractals.- How and when quantum phenomena become real.- Chaotic dynamics in a periodically driven anharmonic oscillator.- Coherent and incoherent dynamics in a periodically driven bistable system.- The Ehrenfest theorem for Markov diffusions.- The quantum state diffusion model, asymptotic solutions, thermal equilibrium and Heisenberg picture.- Stochastic representation of quantum dynamics.- Level repulsion and exceptional points.- Type-II intermittency in the presence of additive and multiplicative noise.- Aspects of Liouville integrability in quantum mechanics.- KAM techniques for time dependent quantum systems.- Dissipation and noise in quantum mechanics.- Irregular scattering, number theory, and statistical mechanics.- Band random matrices, kicked rotator and disordered systems.- Robust scarred states.- The quasiclassical statistical description of quantum dynamical systems and quantum chaos.- Quantum measurement by quantum brain.- Time reversal and Gaussian measures in quantum physics.- Stochastic resonance in bistable systems with fluctuating barriers.- List of participants.