The Transition to Chaos

1. Front Matter

   Pages i-xviii

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2. Overview

   • Linda E. Reichl

   Pages 1-12

3. Fundamental Concepts

   • Linda E. Reichl

   Pages 13-57

4. Area-Preserving Maps

   • Linda E. Reichl

   Pages 58-133

5. Global Properties

   • Linda E. Reichl

   Pages 134-188

6. Random Matrix Theory

   • Linda E. Reichl

   Pages 189-236

7. Bounded Quantum Systems

   • Linda E. Reichl

   Pages 237-292

8. Manifestations of Chaos in Quantum Scattering Processes

   • Linda E. Reichl

   Pages 293-347

9. Semiclassical Theory—Path Integrals

   • Linda E. Reichl

   Pages 348-400

10. Time-Periodic Systems

    • Linda E. Reichl

    Pages 401-473

11. Stochastic Manifestations of Chaos

    • Linda E. Reichl

    Pages 474-485

12. Back Matter

    Pages 486-675

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Based on courses given at the universities of Texas in Austin, and California in San Diego, this book deals with the basic mechanisms that determine the dynamic evolution of classical and quantum systems. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; it continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and it concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature. Problems at the ends of chapters help students clarify their understanding. In this new edition, the presentation will be brought up to date throughout, and a new chapter on open quantum systems will be added.

• chaos
• open quantum system
• path integral

From the reviews of the second edition:

"This book is an expanded and updated version … from a previous edition and reviews results on the manifestation of chaos in classical and quantum mechanics. … A very wide range of topics is covered in the book, which thus can be used as preliminary reading for research areas … . The book can also be considered as a helpful companion both for mathematicians and for physicists. … Many technical details and background notions can be found in a rich complement of appendices." (Guido Gentile, Mathematical Reviews, Issue 2006 c)

• Department of Physics and Center for Statistical Mechanics and Complex Systems, University of Texas at Austin, Austin, USA

  Linda E. Reichl

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