标题： 多维首次通过时间的近似计算 显示英文标题

标题： Approximate calculation of multidimensional first passage times

摘要： 对在保守力作用下扩散过程的一般多维势垒穿越问题进行研究，目的是开发可处理的近似方法。 特别关注了随机微分方程的不同统计解释的影响，以及近似方法与一维问题已知精确解之间的关系。 从一个合理但启发式的简化假设出发，开发出该问题的一维解。 然后通过引入进一步的近似，得到一系列越来越简单的表达式，最终得出Langer（Ann. Phys. 54, 258 (1969))和其他人的经典结果。 通过与模拟结果的比较，对二维问题进行了各种近似的测试，发现一维近似能够捕捉到大部分非阿伦尼乌斯的能量势垒依赖性，这种依赖性在Langer近似中丢失了，而一维近似在大势垒极限情况下仍会收敛到后者。 显示英文摘要

摘要： The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different statistical interpretations of the stochastic differential equation and to the relation between the approximations and the known, exact solutions to the one-dimensional problem. Beginning with a reasonable, but heuristic, simplifying assumption, a one-dimensional solution to the problem is developed. This is then simplified by introducing further approximations resulting in a sequence of increasingly simple expressions culminating in the classic result of Langer(Ann. Phys. 54, 258 (1969)) and others. The various approximations are tested on two dimensional problems by comparison to simulation results and it is found that the one-dimensional approximations capture most of the non-Arrhenius dependence on the energy barrier which is lost in the Langer approximation while still converging to the latter in the large-barrier limit.