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

書誌事項

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

J. Bellissard ... [et al.] ; editor, S. Graffi

(Lecture notes in mathematics, 1589 . Fondazione C.I.M.E., Firenze)

Springer-Verlag, c1994

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タイトル別名

Transition to chaos in classical and quantum mechanics : Montecatini Terme, 1991

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注記

"This volume collects the texts of two series of 8 lectures ... given at the C.I.M.E. Session on 'Transition to Chaos in Classical and Quantum Systems'"--Foreword

Includes bibliographical references

内容説明・目次

内容説明

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 Schroedinger 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.

目次

Non commutative methods in semiclassical analysis.- Equidistribution of periodic orbits: An overview of classical VS quantum results.- Action minimizing orbits in hamiltomian systems.

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