ENGLISH

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

By Sandro Graffi , Mirko Degli Esposti , Sandro Graffi (eds.) , Jean Bellissard , Giovanni Forni , Stefano Isola , John N. Mather (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1994
ISBN
978-3-540-58416-2, 978-3-540-48782-1
DOI
10.1007/BFb0074073
Language
english
Format
PDF
Filesize
3 MB (3281763 bytes)
Series
Lecture Notes in Mathematics 1589
Edition
1
Pages
196\196
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Analysis; Differential Geometry; Quantum ComputingInformation and Physics; Quantum Physics

Description

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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