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Quantum Signatures of Chaos

  • Textbook
  • © 2001

Overview

Authors:
  1. Fritz Haake

    1. Institut für Theoretische Physik, Fachbereich 7, Physik, University of Essen, Essen, Germany

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  • This book is now well established as a textbook in this rapidly developing field of research
  • The new edition is much enlarged and covers a host of new results
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Synergetics (SSSYN, volume 54)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XX
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  2. Introduction

    • Fritz Haake
    Pages 1-13

  3. Time Reversal and Unitary Symmetries

    • Fritz Haake
    Pages 15-36

  4. Level Repulsion

    • Fritz Haake
    Pages 37-45

  5. Random-Matrix Theory

    • Fritz Haake
    Pages 47-118

  6. Level Clustering

    • Fritz Haake
    Pages 119-139

  7. Level Dynamics

    • Fritz Haake
    Pages 141-219

  8. Quantum Localization

    • Fritz Haake
    Pages 221-249

  9. Semiclassical Roles for Classical Orbits

    • Fritz Haake
    Pages 251-322

  10. Dissipative Systems

    • Fritz Haake
    Pages 323-390

  11. Superanalysis for Random-Matrix Theory

    • Fritz Haake
    Pages 391-460

  12. Back Matter

    Pages 461-479
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Keywords

About this book

The warm reception of the first edition, as well as the tumultuous development of the field of quantum chaos have tempted me to rewrite this book and include some of the important progress made during the past decade. Now we know that quantum signatures of chaos are paralleled by wave signa­ tures. Whatever is undergoing wavy space-time variations, be it sound, electro­ magnetism, or quantum amplitudes, each shows exactly the same manifestations of chaos. The common origin is nonseparability of the pertinent wave equation; that latter "definition" of chaos, incidentally, also applies to classical mechanics if we see the Hamilton-Jacobi equation as the limiting case of a wave equation. At any rate, drums, concert halls, oscillating quartz blocks, microwave and opti­ cal oscillators, electrons moving ballistically or with impurity scattering through mesoscopic devices all provide evidence and data for wave or quantum chaos. All of these systems have deep analogies with billiards, much as the latter may have appeared of no more than academic interest only a decade ago. Of course, molec­ ular, atomic, and nuclear spectroscopy also remain witnesses of chaos, while the chromodynamic innards of nucleons are beginning to attract interest as methods of treatment become available.

Reviews

"The book can be recommended both as a textbook and a review of the subject. The rich set of references allows one to catch up with the current literature. Exercises facilitate the study and will be of use to the lecturer. It can be a base of a solid graduate theoretical course in quantum chaos." (Pure and Applied Geophysics, 160, 2003)

"In summary, this is definitely an essential reference book for the specialist. It will also ably serve someone entering the field for the first time who needs to learn the theoretical state of the art in detail." (G. Summy (University of Oxford), Contemporary Physics 2002, vol. 43, page 232)

Authors and Affiliations

  • Institut für Theoretische Physik, Fachbereich 7, Physik, University of Essen, Essen, Germany

    Fritz Haake

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