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.
Received: 26 December 2006
Accepted manuscript online:
(Probability theory, stochastic processes, and statistics)
Fund: 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).
Cite this article:
Deng Mao-Lin(邓茂林) and Zhu Wei-Qiu(朱位秋) Energy diffusion controlled reaction rate in dissipative Hamiltonian systems 2007 Chinese Physics 16 1510
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