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AuthorBellissard, Jean. author
TitleTransition to Chaos in Classical and Quantum Mechanics [electronic resource] : 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 Jean Bellissard, Mirko Degli Esposti, Giovanni Forni, Sandro Graffi, Stefano Isola, John N. Mather ; edited by Sandro Graffi
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1994
Connect tohttp://dx.doi.org/10.1007/BFb0074073
Descript VIII, 196 p. online resource

SUMMARY

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 Schrรถdinger 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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Differential geometry Quantum physics Quantum computers Spintronics Mathematics Analysis Differential Geometry Quantum Information Technology Spintronics Quantum Physics



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