dorsal/arxiv
View SchemaHypersensitivity and chaos signatures in the quantum baker's maps
| Authors | A. J. Scott, Todd A. Brun, Carlton M. Caves, Ruediger Schack |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606102 |
| URL | https://arxiv.org/abs/quant-ph/0606102 |
| DOI | 10.1088/0305-4470/39/43/002 |
| Journal | J. Phys. A 39, 13405 (2006) |
Abstract
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead 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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"abstract": "Classical chaotic systems are distinguished by their sensitive dependence on\ninitial conditions. The absence of this property in quantum systems has lead to\na number of proposals for perturbation-based characterizations of quantum\nchaos, including linear growth of entropy, exponential decay of fidelity, and\nhypersensitivity to perturbation. All of these accurately predict chaos in the\nclassical limit, but it is not clear that they behave the same far from the\nclassical realm. We investigate the dynamics of a family of quantizations of\nthe baker\u0027s map, which range from a highly entangling unitary transformation to\nan essentially trivial shift map. Linear entropy growth and fidelity decay are\nexhibited by this entire family of maps, but hypersensitivity distinguishes\nbetween the simple dynamics of the trivial shift map and the more complicated\ndynamics of the other quantizations. This conclusion is supported by an\nanalytical argument for short times and numerical evidence at later times.",
"arxiv_id": "quant-ph/0606102",
"authors": [
"A. J. Scott",
"Todd A. Brun",
"Carlton M. Caves",
"Ruediger Schack"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1088/0305-4470/39/43/002",
"journal_ref": "J. Phys. A 39, 13405 (2006)",
"title": "Hypersensitivity and chaos signatures in the quantum baker\u0027s maps",
"url": "https://arxiv.org/abs/quant-ph/0606102"
},
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