论文标题
通过过度抑制Langevin方程在确切可解的模型中的过渡路径集合分析
Analysis of Transition Path Ensemble in the Exactly Solvable Models via Overdamped Langevin Equation
论文作者
论文摘要
在两个州之间的系统过渡是自然科学中一个重要但困难的问题。在本文中，我们研究了过渡路径集合框架中的过渡问题。使用过度阻尼的langevin方法，我们介绍了过渡概率的路径积分公式，并在过渡路径空间中获得最小动作路径的方程。对于过渡路径集合中的有效采样，我们得出条件抑制了langevin方程。在两个确切的可解决模型（即自由粒子系统和谐波系统）中，我们介绍了条件概率密度的表达以及条件Langevin方程和最小动作路径的显式解决方案。分析结果证明了条件Langevin方程与过渡中所需的概率分布的一致性。可以证实，条件兰格文方程是采样过渡路径集合的有效工具，最小动作原理实际上导致了最可能的路径。
Transition of a system between two states is an important but difficult problem in natural science. In this article we study the transition problem in the framework of transition path ensemble. Using the overdamped Langevin method, we introduce the path integral formulation of the transition probability and obtain the equation for the minimum action path in the transition path space. For the effective sampling in the transition path ensemble, we derive a conditional overdamped Langevin equation. In two exactly solvable models, the free particle system and the harmonic system, we present the expression of the conditional probability density and the explicit solutions for the conditional Langevin equation and the minimum action path. The analytic results demonstrate the consistence of the conditional Langevin equation with the desired probability distribution in the transition. It is confirmed that the conditional Langevin equation is an effective tool to sample the transition path ensemble, and the minimum action principle actually leads to the most probable path.
