Graffi 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
1994
ISBN: 978-3-540-48782-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1589, 196 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Graffi, Sandro

Weitere Mitwirkende

Bellissard, J.

Degli Esposti, M.

Forni, G.

Graffi, Sandro

Isola, S.

Mather, J.N.

Inhaltsverzeichnis

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