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  • Hypersensitivity and chaos signatures in the quantum baker’s maps

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    Author(s)
    Scott, A
    Brun, Todd
    Caves, Carlton
    Schack, Rüdiger
    Griffith University Author(s)
    Scott, Andrew J.
    Year published
    2006
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    Abstract
    Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an ...
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    Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has led to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This conclusion is supported by an analytical argument for short times and numerical evidence at later times.
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    Journal Title
    Journal of Physics A: Mathematical and General
    Volume
    39
    Issue
    43
    Publisher URI
    https://iopscience.iop.org/journal/1751-8121
    DOI
    https://doi.org/10.1088/0305-4470/39/43/002
    Copyright Statement
    © 2006 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Quantum Physics not elsewhere classified
    Mathematical Sciences
    Physical Sciences
    Publication URI
    http://hdl.handle.net/10072/22681
    Collection
    • Journal articles

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