Classical Physics

In the previous chapter we listed some notions of the mathematical theory of stochastic processes. The present chapter aims to endow the theory with some physical content. To this end, we use a Brownian particle immersed in a fluid as our paradigmatic mod

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THE FRONTIERS COLLECTION Series Editors: D. Dragoman M. Dragoman A.C. Elitzur M.P. Silverman

J. Tuszynski H.D. Zeh

The books in this collection are devoted to challenging and open problems at the forefront of modern physics and related disciplines, including philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science. It is intended to encourage scientists in all areas to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, time and consciousness - the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge.

Quantum Mechanics and Gravity ByM. Sachs Mind, Matter and Quantum Mechanics ByH. Stapp Quantum-Classical Correspondence By A.O. Bolivar Quantum-Classical Analogies By D. Dragoman and M. Dragoman Quo Vadis Quantum Mechanics? Edited by A. C. Elitzur, S. Dolev, N. Kolenda

Series homepage - springeronline.com

A. O. Bolivar

QUANTUMCLASSICAL CORRESPONDENCE Dynamical Quantization and the Classical Limit

With 14 Figures

i

Springer

Dr. A. O. Bolivar Instituto Cultural Eudoro de Sousa, CEP: 72.221-970 Caixa Postal: 7316 Ceilandia, DF, Brazil email: [email protected]

Series Editors: Prof. Daniela Dragoman University of Bucharest, Physics Faculty, Solid State Chair, PO Box MG-ll, 76900 Bucharest, Romania email: [email protected]

Prof. Mircea Dragoman National Research and Development Institute in Microtechnology, PO Box 38-160, 023573 Bucharest, Romania email: [email protected]

Prof. Avshalom C. Elitzur Bar-Han University, Unit of Interdisciplinary Studies, 52900 Ramat-Gan, Israel email: [email protected]

Prof. Mark P. Silverman Department of Physics, Trinity College, Hartford, CT 06106, USA email: [email protected]

Prof. Jack Tuszynski University of Alberta, Department of Physics, Edmonton, AB, T6G 2}1, Canada email: [email protected]

Prof. H. Dieter Zeh University of Heidelberg, Institute ofTheoretical Physics, Philosophenweg 19, 69120 Heidelberg, Germany email: [email protected] Coverfigure: Image showing emerging morphological features during etching reactions, modelled by atomistic cellular automata. Courtesy of M.A. Gosalvez and R.M. Nieminen, Helsinki University of Technology.

ISSN 1612-3018 ISBN 978-3-642.-05765-6 Cataloging-in-Publication Data. Bolivar, A.O., 1972- . Quantum-classical correspondence: dynamical quantization and the classicallimit/ A.O. Bolivar. p.cm. - (The frontiers collection, ISSN 1612-3018) Includes bibliographical references and index. 1. Correspondence principle (Quantum mechanics) 2. Stoc