### 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 | |

State | Published - Feb 1 1993 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*173*(2), 148-152. https://doi.org/10.1016/0375-9601(93)90178-3

**Temporal crossover from classical to quantum behavior : a Markov-chain approach.** / Lai, Ying-Cheng; Ott, Edward; Grebogi, Celso.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 173, no. 2, pp. 148-152. https://doi.org/10.1016/0375-9601(93)90178-3

}

TY - JOUR

T1 - Temporal crossover from classical to quantum behavior

T2 - a Markov-chain approach

AU - Lai, Ying-Cheng

AU - Ott, Edward

AU - Grebogi, Celso

PY - 1993/2/1

Y1 - 1993/2/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0001758524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001758524&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(93)90178-3

DO - 10.1016/0375-9601(93)90178-3

M3 - Article

AN - SCOPUS:0001758524

VL - 173

SP - 148

EP - 152

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2

ER -