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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

  • Book
  • © 1994

Overview

Authors:
  1. Jean Bellissard
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  2. Mirko Degli Esposti
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  3. Giovanni Forni
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  4. Sandro Graffi
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  5. Stefano Isola
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  6. John N. Mather
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Editors:
  1. Sandro Graffi
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1589)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-V
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  2. Non commutative methods in semiclassical analysis

    • Jean Bellissard
    Pages 1-64

  3. Equidistribution of periodic orbits: An overview of classical VS quantum results

    • Mirko Degli Esposti, Sandro Graffi, Stefano Isola
    Pages 65-91

  4. Action minimizing orbits in hamiltomian systems

    • John N. Mather, Giovanni Forni
    Pages 92-186

  5. Back Matter

    Pages 188-192
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Transition to Chaos in Classical and Quantum Mechanics

  • Book Subtitle: 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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0074073

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58416-2Published: 26 September 1994

  • eBook ISBN: 978-3-540-48782-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 196

  • Topics: Analysis, Differential Geometry, Quantum Information Technology, Spintronics, Quantum Physics

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