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Classical Nonintegrability, Quantum Chaos : DMV Seminar - A. Knauf

Classical Nonintegrability, Quantum Chaos

DMV Seminar

Paperback Published: 20th March 1997
ISBN: 9783764357085
Number Of Pages: 102

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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.

Introductionp. 1
Dynamical Zeta Functionsp. 3
Irregular Scatteringp. 21
Quantum Chaosp. 47
Ergodicity and Mixingp. 75
Expanding Mapsp. 79
Liouville Surfacesp. 87
Participantsp. 94
Additional Talksp. 96
Indexp. 97
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764357085
ISBN-10: 3764357088
Series: DMV Seminar
Audience: General
Format: Paperback
Language: English
Number Of Pages: 102
Published: 20th March 1997
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.39 x 15.6  x 0.56
Weight (kg): 0.16