Transition-event durations in one-dimensional activated processes

Bin W. Zhang, David Jasnow, Daniel M. Zuckerman

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Abstract

Despite their importance in activated processes, transition-event durations-which are much shorter than first passage times-have not received a complete theoretical treatment. The authors therefore study the distribution ρ b (t) of durations of transition events over a barrier in a one-dimensional system undergoing overdamped Langevin dynamics. The authors show that ρ b (t) is determined by a Fokker-Planck equation with absorbing boundary conditions and obtain a number of results, including (i) the analytic form of the asymptotic short-time transient behavior, which is universal and independent of the potential function; (ii) the first nonuniversal correction to the short-time behavior leading to an estimate of a key physical time scale; (iii) following previous work, a recursive formulation for calculating, exactly, all moments of ρ b based solely on the potential function-along with approximations for the distribution based on a small number of moments; and (iv) a high-barrier approximation to the long-time (t→∞) behavior of ρ b (t). The authors also find that the mean event duration does not depend simply on the barrier-top frequency (curvature) but is sensitive to details of the potential. All of the analytic results are confirmed by transition-path- sampling simulations implemented in a novel way. Finally, the authors discuss which aspects of the duration distribution are expected to be general for more complex systems.

Original languageEnglish (US)
Article number074504
JournalJournal of Chemical Physics
Volume126
Issue number7
DOIs
StatePublished - Mar 5 2007

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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