### 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 HBAR as t(max) approximately HBAR(-mu). 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 |
---|---|

Pages (from-to) | 148-152 |

Number of pages | 5 |

Journal | Physics Letters A |

Volume | 173 |

Issue number | 2 |

Publication status | Published - 1 Feb 1993 |

### Keywords

- HAMILTONIAN-SYSTEMS
- TREE MODEL
- TRANSPORT

### Cite this

*Physics Letters A*,

*173*(2), 148-152.

**TEMPORAL CROSSOVER FROM CLASSICAL TO QUANTUM BEHAVIOR - A MARKOV-CHAIN APPROACH.** / LAI, Y C ; OTT, E ; GREBOGI, C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 173, no. 2, pp. 148-152.

}

TY - JOUR

T1 - TEMPORAL CROSSOVER FROM CLASSICAL TO QUANTUM BEHAVIOR - A MARKOV-CHAIN APPROACH

AU - LAI, Y C

AU - OTT, E

AU - GREBOGI, C

AU - Lai, Ying-Cheng

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 HBAR as t(max) approximately HBAR(-mu). 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 HBAR as t(max) approximately HBAR(-mu). 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.

KW - HAMILTONIAN-SYSTEMS

KW - TREE MODEL

KW - TRANSPORT

M3 - Article

VL - 173

SP - 148

EP - 152

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 2

ER -