Titlebook: Chaos — The Interplay Between Stochastic and Deterministic Behaviour; Proceedings of the X Piotr Garbaczewski,Marek Wolf,Aleksander Weron C

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Schriften zur UnternehmensentwicklungIn this paper, several recent results on classical and quantum chaotic scattering by the author and collaborators are reviewed. New phenomena regarding qualitative changes of scattering characteristics as parameter changes in the classical context and quantum manifestation of chaotic scattering are discussed.

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Positive Emotionalit?t in OrganisationenNew sufficient conditions for asymptotic stability of Markov operators on metric spaces are presented. These criterion are applied to iterated function systems and stochastic differential equations with Poisson type perturbations.

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Anomalous diffusion, spontaneous localizations and the correspondence principle,We show that the equivalence between quantum and classical physics can be obtained, in the proper limit, by using arguments of ordinary statistical mechanics. It is argued that conditions of statistical mechanics as non ordinary as anomalous diffusion might produce the breakdown of this equivalence

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Oration

Classical and quantum chaotic scattering,In this paper, several recent results on classical and quantum chaotic scattering by the author and collaborators are reviewed. New phenomena regarding qualitative changes of scattering characteristics as parameter changes in the classical context and quantum manifestation of chaotic scattering are discussed.

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Quantum open systems as random classical dynamical systems,incide with correlations of the quantum oscillator in a heat bath. In this way we replace a quantum non-commutative problem by a classical commutative one. In this framework we discuss briefly dissipation, noise,spontaneous localization and decoherence in quantum mechanics.

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Eigenfunction expansions for time dependent hamiltonians,pansion in eigenfunctions of a generalized quasienergy operator. We discuss a conjecture on the extension of the adiabatic theorem to this type of systems, which gives a procedure for the physical preparation of Floquet states. *** DIRECT SUPPORT *** A3418380 00004

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Entropy and quantum characteristic exponents. steps towards a quantum pesin theory,provide an intuitive framework to construct the corresponding notions in quantum mechanics..Rigorous existence conditions obtained for quantum characteristic exponents and a definition of quantum entropy based on the Brin-Katok construction are steps towards a quantum ergodic theory, where a rigorous definition of quantum chaos may be established.