Temporal crossover from classical to quantum behavior: a Markov-chain approach

Ying Cheng Lai; Edward Ott; Celso Grebogi

doi:10.1016/0375-9601(93)90178-3

Temporal crossover from classical to quantum behavior: a Markov-chain approach

Ying Cheng Lai
, Edward Ott
, Celso Grebogi

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Previous renormalization group analyses that for chaotic systems near their critical points, the crossover time from classical to quantum behaviors scales with the Planck constant h{stroke} as t_max∼h{stroke}^-μ. We argue that the same scaling relation also holds for typical two-degrees-of-freedom and time-independent chaotic Hamiltonian systems. Our analysis makes use of a self-similar Markov-chain model which was previously used to qualitatively explain the algebraic decay law in Hamiltonian systems.

Original language	English (US)
Pages (from-to)	148-152
Number of pages	5
Journal	Physics Letters A
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/0375-9601(93)90178-3
State	Published - Feb 1 1993
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/0375-9601(93)90178-3

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title = "Temporal crossover from classical to quantum behavior: a Markov-chain approach",

abstract = "Previous renormalization group analyses that for chaotic systems near their critical points, the crossover time from classical to quantum behaviors scales with the Planck constant h\{stroke\} as tmax∼h\{stroke\}-μ. We argue that the same scaling relation also holds for typical two-degrees-of-freedom and time-independent chaotic Hamiltonian systems. Our analysis makes use of a self-similar Markov-chain model which was previously used to qualitatively explain the algebraic decay law in Hamiltonian systems.",

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N2 - Previous renormalization group analyses that for chaotic systems near their critical points, the crossover time from classical to quantum behaviors scales with the Planck constant h{stroke} as tmax∼h{stroke}-μ. We argue that the same scaling relation also holds for typical two-degrees-of-freedom and time-independent chaotic Hamiltonian systems. Our analysis makes use of a self-similar Markov-chain model which was previously used to qualitatively explain the algebraic decay law in Hamiltonian systems.

AB - Previous renormalization group analyses that for chaotic systems near their critical points, the crossover time from classical to quantum behaviors scales with the Planck constant h{stroke} as tmax∼h{stroke}-μ. We argue that the same scaling relation also holds for typical two-degrees-of-freedom and time-independent chaotic Hamiltonian systems. Our analysis makes use of a self-similar Markov-chain model which was previously used to qualitatively explain the algebraic decay law in Hamiltonian systems.

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Temporal crossover from classical to quantum behavior: a Markov-chain approach

Abstract

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