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. 1st ed. 1994

種類:

電子ブック

責任表示:

edited by Sandro Graffi

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994

著者名:

• Graffi, Sandro.
• SpringerLink (Online service)

シリーズ名:

C.I.M.E. Foundation Subseries ; 1589

ISBN:

9783540487821 [3540487824]    

注記:

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

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