Quantum Signatures of Chaos
This by now classic text provides an excellent introduction and survey to the continuously expanding field of quantum chaos . The topics treated include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish r
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d Programme Advisory Board Dan Braha, New England Complex Systems Institute and University of Massachusetts Dartmouth, USA ` , Center for Complex Systems Studies, Kalamazoo College, USA and Hungarian Academy of P´eter Erdi Sciences, Budapest, Hungary
Karl Friston, Institute of Cognitive Neuroscience, University College London, London, UK Hermann Haken, Center of Synergetics, University of Stuttgart, Stuttgart, Germany Janusz Kacprzyk, System Research, Polish Academy of Sciences, Warsaw, Poland Scott Kelso, Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, USA J¨urgen Kurths, Nonlinear Dynamics Group, University of Potsdam, Potsdam, Germany Linda Reichl, Center for Complex Quantum Systems, University of Texas, Austin, USA Peter Schuster, Theoretical Chemistry and Structural Biology, University of Vienna, Vienna, Austria Frank Schweitzer, System Design, ETH Zurich, Zurich, Switzerland Didier Sornette, Entrepreneurial Risk, ETH Zurich, Zurich, Switzerland
Springer Series in Synergetics Founding Editor: H. Haken
The Springer Series in Synergetics was founded by Herman Haken in 1977. Since then, the series has evolved into a substantial reference library for the quantitative, theoretical and methodological foundations of the science of complex systems. Through many enduring classic texts, such as Haken’s Synergetics and Information and Self-Organization, Gardiner’s Handbook of Stochastic Methods, Risken’s The Fokker Planck-Equation or Haake’s Quantum Signatures of Chaos, the series has made, and continues to make, important contributions to shaping the foundations of the field. The series publishes monographs and graduate-level textbooks of broad and general interest, with a pronounced emphasis on the physico-mathematical approach.
Fritz Haake
Quantum Signatures of Chaos Third Revised and Enlarged Edition
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Prof. Dr. Fritz Haake Universit¨at Duisburg-Essen FB 7 Physik Universit¨atsstr. 5 45117 Essen Germany [email protected] [email protected]
ISBN 978-3-642-05427-3 e-ISBN 978-3-642-05428-0 DOI 10.1007/978-3-642-05428-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010920833 c Springer-Verlag Berlin Heidelberg 2010, 2000, 1991 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant prote
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