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 [and others] ; editor, S. Graffi.

Contributor(s): Bellissard, J. (Jean) | Graffi, S. (Sandro), 1943- | Centro internazionale matematico estivo
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1589.Publisher: Berlin ; New York : Springer-Verlag, ©1994Description: 1 online resource (192 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540487821; 3540487824Subject(s): Quantum theory | Chaotic behavior in systems | Théorie quantique -- Congrès | Chaos -- Congrès | Chaotic behavior in systems | Quantum theory | Chaos | Kwantummechanica | Chaostheorie | Kongress | Dynamisches System | Chaotisches System | Quantenchaos | Quantenmechanik | Sistemas DinamicosGenre/Form: Electronic books. Additional physical formats: Print version:: Transition to chaos in classical and quantum mechanics.DDC classification: 530.1/2 LOC classification: QA3 | .L28 no. 1589 | QC174.12Other classification: 31.55 Online resources: Click here to access online
Contents:
Non commutative methods in semiclassical analysis -- Equidistribution of periodic orbits: An overview of classical VS quantum results -- Action minimizing orbits in hamiltomian systems.
Action note: digitized 2010 committed to preserveSummary: 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 Schrdinger 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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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 Schrdinger 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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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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