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Classical Nonintegrability, Quantum Chaos

With a contribution by Viviane Baladi

  • Andreas Knauf
  • Yakov G. Sinai
  • Viviane Baladi

Part of the DMV Seminar book series (OWS, volume 27)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 1-2
  3. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 3-20
  4. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 21-46
  5. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 47-74
  6. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 75-78
  7. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 79-85
  8. Andreas Knauf, Yakov G. Sinai, Viviane Baladi
    Pages 87-93
  9. Back Matter
    Pages 94-98

About this book

Introduction

Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin­ tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead­ ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter­ ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.

Keywords

Finite Invariant analysis ergodic theory function geometry mathematical physics mathematics nonlinear dynamics quantum chaos theorem

Authors and affiliations

  • Andreas Knauf
    • 1
  • Yakov G. Sinai
    • 2
  • Viviane Baladi
    • 3
  1. 1.Fachbereich 3 - Mathematik, MA 7-2Technische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA
  3. 3.Section de MathématiquesUniversité de Genève1211 Genève 24Switzerland

Bibliographic information

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