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Overview

  • Linda E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)

Abstract

This book is about the nonlinear dynamics of conservative classical and quantum systems. Although classical and quantum mechanics are now rather old subjects (classical mechanics is over 300 years old and quantum mechanics is over 90 years old), the mechanisms affecting their dynamical evolution have only recently been understood. In this book we will focus on the transition to chaos in classical systems and the manifestations of chaos in quantum systems. One of the important discoveries in quantum physics in recent years is that the information content of quantum systems is extremized when the underlying classical system undergoes a transition to chaos. The information content approaches that of a system whose dynamics is governed by a random Hamiltonian matrix chosen to extremize information. For this reason, random matrix theory has become essential to quantum chaos theory. In this book we include a self-contained discussion of the random matrix theory and supersymmetry techniques necessary for the study of the statistical properties of quantum systems. Toward the end of the book, we include a short chapter showing that the manifestations of chaos can also appear in stochastic systems.

Keywords

Phase Space Quantum System Chaotic System Random Matrix Theory Nonlinear Resonance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

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

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