Zhang Bin W, Jasnow David, Zuckerman Daniel M
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
J Chem Phys. 2007 Feb 21;126(7):074504. doi: 10.1063/1.2434966.
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 rhob(t) of durations of transition events over a barrier in a one-dimensional system undergoing overdamped Langevin dynamics. The authors show that rhob(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 rhob 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-->infinity) behavior of rhob(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.
尽管过渡事件持续时间在活化过程中很重要，但它比首次穿越时间短得多，尚未得到完整的理论处理。因此，作者研究了在经历过阻尼朗之万动力学的一维系统中越过势垒的过渡事件持续时间的分布ρb(t)。作者表明，ρb(t)由具有吸收边界条件的福克 - 普朗克方程决定，并获得了许多结果，包括：(i) 渐近短时间瞬态行为的解析形式，它是通用的，与势函数无关；(ii) 对短时间行为的第一个非通用修正，从而得到一个关键物理时间尺度的估计；(iii) 沿用之前的工作，一种仅基于势函数精确计算ρb所有矩的递归公式，以及基于少量矩的分布近似；(iv) 对ρb(t)长时间（t→∞）行为的高势垒近似。作者还发现平均事件持续时间不仅仅取决于势垒顶部频率（曲率），还对势的细节敏感。所有解析结果都通过以一种新颖方式实现的过渡路径采样模拟得到了证实。最后，作者讨论了持续时间分布的哪些方面对于更复杂的系统预计是通用的。
