The Transition to Chaos

Conservative Classical Systems and Quantum Manifestations

  • Linda E. Reichl

Part of the Institute for Nonlinear Science book series (INLS)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Linda E. Reichl
    Pages 1-12
  3. Linda E. Reichl
    Pages 13-57
  4. Linda E. Reichl
    Pages 58-133
  5. Linda E. Reichl
    Pages 134-188
  6. Linda E. Reichl
    Pages 189-236
  7. Linda E. Reichl
    Pages 237-292
  8. Linda E. Reichl
    Pages 348-400
  9. Linda E. Reichl
    Pages 401-473
  10. Linda E. Reichl
    Pages 474-485
  11. Back Matter
    Pages 486-675

About this book


This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes. Specific discussions include:

• Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior.

• Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems.

• Random matrix theory and supersymmetry.

The book is divided into several parts. Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems. Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques. Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively. Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapter 9 discusses the quantum mechanics of systems driven by time-periodic forces. Chapter 10 reviews some recent work on the stochastic manifestations of chaos.

The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature. End of chapter problems help students clarify their understanding. In this new edition, the presentation has been brought up to date throughout, and a new chapter on open quantum systems has been added.

About the author:

Linda E. Reichl, Ph.D., is a Professor of Physics at the University of Texas at Austin and has served as Acting Director of the Ilya Prigogine Center for Statistical Mechanics and Complex Systems since 1974. She is a Fellow of the American Physical Society and currently is U.S. Editor of the journal Chaos, Solitons, and Fractals.


chaos open quantum system path integral

Authors and affiliations

  • Linda E. Reichl
    • 1
  1. 1.Department of Physics and Center for Statistical Mechanics and Complex SystemsUniversity of Texas at AustinAustinUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3163-4
  • Online ISBN 978-1-4757-4350-0
  • Series Print ISSN 1431-4673
  • About this book