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    Chaotic dynamics in classical and quantum mechanical systems

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    Author
    Han, Pin, 1967-
    Issue Date
    1996
    Keywords
    Physics, General.
    Advisor
    Parmenter, Robert H.
    
    Metadata
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    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    This dissertation describes mainly researches on the chaotic properties of some classical and quantum mechanical systems. New phenomena like the three-dimensional uniform stochastic web and multiply riddled behavior are presented with numerical results. In the introduction, a short history and basic principles about chaotic dynamical systems are reviewed, which include the concepts of Lyapunov exponents and Poincare sections. In Chapter 2, we first discuss the Hamiltonian system, followed by the perturbation and KAM theory, then introduce Arnold diffusion and the existence of stochastic webs. We close this chapter with a system which can generate a three-dimensional uniform stochastic web. In Chapter 3, the relationship between deterministic chaos and quantum mechanics is studied. A quantum mechanical system called the tetrahedral array of Josephson junctions in which the deterministic chaos can exist is presented. At the end, we generalize such systems to any dimension and expect that chaos should survive in a higher dimensional case. In Chapter 4, in addition to the introduction of the riddled behavior, three examples in which multiply riddled behavior can occur are given and illustrated by graphs. The generalization of these systems is also made and we still expect that multiply riddled behavior will exist in these generalized systems containing more degrees of freedom.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Physics
    Degree Grantor
    University of Arizona
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