随机跃迁：在早期阶段，跨越较高能垒的路径可能占主导
Stochastic transitions: Paths over higher energy barriers can dominate in the early stages
AI总结：
研究随机跃迁中时间尺度对路径选择的影响，证明短时间内跨越高能垒但相空间距离更短的路径可能占主导，并扩展 gMAM 算法以确定不同时间尺度下的最可能路径。
摘要：
许多物理、化学和生物系统的时间演化，都可以通过描述所研究系统的势能面各极小值之间的随机跃迁来建模。我们表明，在系统存在两条（或更多）可能路径的情况下，可用于发生跃迁的时间至关重要。用于确定跃迁速率的著名反应速率理论结果适用于长时间极限。然而，在短时间内，系统反而可能以高得多的概率选择跨越较高的能垒，只要其在相空间中需要行进的距离更短。我们构建了两个简单模型来说明这一普遍现象。我们还提出了对 Vanden-Eijnden 和 Heymann [J. Chem. Phys. 128, 061103 (2008)] 的 gMAM 算法的扩展，以确定短时间和长时间下的最可能路径。
英文摘要：
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of reaction rate theory for determining the rates of the transitions apply in the long-time limit. However, at short times, the system can instead choose to pass over higher energy barriers with much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also present an extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. {\bf 128}, 061103 (2008)] to determine the most likely path at both short and long times.
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