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)
Year published
2006
Metadata
Show full item recordAbstract
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 ...
View more >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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View more >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.
View less >
Journal Title
Journal of Physics A: Mathematical and General
Volume
39
Issue
43
Publisher URI
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