Stochastic Aspects of Classical and Quantum Systems Proceedings of t
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1109 Stochastic Aspects of Classical and Quantum Systems Proceedings of the 2nd French-German Encounter in Mathematics and Physics, held in Marseille, France, March 28 - April 1, 1983
Edited by S. Albeverio, Ph. Combe and M. Sirugue-Collin
Springer-Verlag Berlin Heidelberg New York Tokyo 1985
Editors
Sergio Albeverio Mathematisches Institut, Ruhr-Universitat 4630 Bochum, Federal Republic of Germany Philippe Combe Universite d'Aix-Marseilie II Luminy Marseille, France Madeleine Sirugue-Collin Universite de Provence, Marseille, France
AMS Subject Classification (1980): 60GXX, 60HXX, 60JXX, 81FXX; 34 BXX, 35JXX, 35XX, 73XX, 76XX, 81G20, 82XX, 85XX ISBN 3-540-13914-1 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13914-1 Springer-Verlag New York Heidelberg Berlin Tokyo Library of Congress Cataloging in Publication Data. Main entry under title: Stochastic aspects of classical and quantum systems. (Lecture notes in mathematics; 1109) 1. Stochastic processes-Congresses. 2. Quantum theory-Congresses. I. Albeverio, Sergio. II. Combe, Philippe, 1940-. III. Sirugue-Collin, M. (Madeleine), 1936-. IV. Series: Lecture notes in mathematics (Springer-Verlag); 1109. 0A3.L28 no. 1109 510 s 85-2652 [QC20.7.S81 [530.1'592] ISBN 0-387-13914-1 (U.S.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach 1Bergstr. 2146/3140-543210
Preface In recent years it has been realized by research workers in many different research areas that the traditional rather strict separation between deterministic and stochastic phenomena had to undergo a profound revision. Systems that used to be described and interpreted purely in classical deterministic terms have turned out to have essential stochastic features, and there have been on the other hand serious efforts to give a classical interpretation to some basic stochastic phenomena. As an example of the former we might mention the detailed study of simple dynamical systems exhibiting "strange attractors", as an example of the latter we think of the efforts to construct mechanical models of diffusion processes and hence, via stochastic mechanics, of quantum phenomena. The present workshop, the second in a series of Encounters between mathematicians and mathematical physicists operating in France and in the Federal Republic of Germany, was organized around a central subject belonging to the above area of interactions between classical and probabilistic descriptions of certain "chaotic" natural phenomena. The relation between quantum theory and classical mechanics has many different aspects. Some of t
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