Transition to Chaos in Classical and Quantum Mechanics

Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, July 6–13, 1991

  • Authors
  • Jean Bellissard
  • Mirko Degli Esposti
  • Giovanni Forni
  • Sandro Graffi
  • Stefano Isola
  • John N. Mather
  • Editors
  • Sandro Graffi

Part of the Lecture Notes in Mathematics book series (LNM, volume 1589)

Table of contents

  1. Front Matter
    Pages I-V
  2. Mirko Degli Esposti, Sandro Graffi, Stefano Isola
    Pages 65-91
  3. John N. Mather, Giovanni Forni
    Pages 92-186
  4. Back Matter
    Pages 188-192

About this book

Introduction

The Session was intended to give a broad survey of the mathematical problems arising in the chaotic transition of deterministic dynamical systems, both in classical and quantum mechanics.
The lectures of Mather and Forni thoroughly cover the area- preserving twist maps, and include an up-to-date version of the Aubry-Mather theory.
The lectures of Bellissard describe the quantum aspects: classical limit, localization, spectral properties of the relevant Schrödinger operators and thus represent an exhaus- tive introduction to the mathematics of "quantum chaos".
The lectures of Degli Esposti et al. reviews equidistribu- tion of unstable periodic orbits and classical limit of quantized toral symplectomorphisms.

Keywords

Aubry-Mather sets Non commutative methods classical limit periodic orbits quantum chaos quantum mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0074073
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58416-2
  • Online ISBN 978-3-540-48782-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book