Cambridge University Press, 1995. — 699 p.This volume presents a collection of basic papers, some already published others specially written for this volume, devoted to the study of a new phenomenon, the so-called quantum chaos. This problem arose from the by now, well known, classical dynamical chaos. However, unlike the latter, the study of quantum chaos is still in its early stages, attracting the ever growing interest of many physicists (but, unfortunately, of many fewer, as yet, mathematicians). The original intention, of physicists at least, was mainly to understand the very important generic phenomenon of classical chaos from the viewpoint of the more deep and general quantum mechanics. At first sight it might seem that quantum chaos is simply a particular case of the general phenomenon of dynamical chaos in the well developed ergodic theory of dynamical systems; or it might be a trivial implication of the correspondence principle. Yet, Nature has turned out to be much more tricky, and more interesting! As the present collection of papers clearly shows, there is no classical-like chaos at all in quantum mechanics. On the other hand since Nature, as is commonly accepted, obeys quantum mechanics, what is then the physical meaning of dynamical chaos? As a result of this surprising obstacle, the general situation in the study of quantum chaos, in the present state of research, might be characterized as some confusion and disorganization which is of course a typical situation in the early stages of a new field of scientific research. It greatly stimulates and encourages the active search for new approaches to the problem, quite often without any attempts to reconcile the different conceptions. The primary goal of this collection is just to help in the cure of such a disease of growth. For the reader's convenience we have grouped the papers into four different main topics: a) "Classical chaos and quantum localization" which is the most extensively investigated subject; b) "Atoms in magnetic and microwave fields" which refers also to the laboratory experiments in quantum chaos; c) "Semi-classical approximations" which examines the transition between classical and quantum chaos; and d) "Level statistics and random matrix theory" which describes the relation with the well developed statistical theory of complex quantum systems.
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