中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1510-1515.doi: 10.1088/1009-1963/16/6/003

• GENERAL • 上一篇    下一篇

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

邓茂林, 朱位秋   

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2006-12-26 出版日期:2007-06-20 发布日期:2007-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Key Grant No~10332030), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No~20060335125) and the National Science Foundation for Post-doctoral Scientists of China (Grant No~20060390338).

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

Deng Mao-Lin(邓茂林) and Zhu Wei-Qiu(朱位秋)†   

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
  • Received:2006-12-26 Online:2007-06-20 Published:2007-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Key Grant No~10332030), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No~20060335125) and the National Science Foundation for Post-doctoral Scientists of China (Grant No~20060390338).

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摘要： In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.

Abstract: In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.

Key words: quasi Hamiltonian system, Kramers reaction rate theory, mean first-passage time, stochastic averaging

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.50.-r (Probability theory, stochastic processes, and statistics)