Institut de Physique Théorique, CEA, IPhT CNRS, URA2306, Gif-sur-Yvette, France.
J Chem Phys. 2011 May 7;134(17):174114. doi: 10.1063/1.3586036.
We propose a novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time t(f). These paths are weighted with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a non-local stochastic differential equation. In the limit of short times, we show that this complicated non-solvable equation can be simplified into an approximate local stochastic differential equation. For longer times, the paths generated by this approximate equation do not satisfy the correct statistics, but this can be corrected by an adequate reweighting of the trajectories. In all cases, the paths are statistically independent and provide a representative sample of transition paths. The method is illustrated on the one-dimensional quartic oscillator.
我们提出了一种新的随机方法，用于生成在给定初始状态下开始并在特定时间 t(f) 内结束于给定最终状态的路径。这些路径的权重由过阻尼朗之万动力学给出的概率决定。我们表明这些路径可以通过一个非局部随机微分方程精确地生成。在短时间的极限下，我们表明这个复杂的不可解方程可以简化为一个近似的局部随机微分方程。对于较长的时间，这个近似方程生成的路径不符合正确的统计数据，但通过对轨迹进行适当的重新加权可以进行修正。在所有情况下，路径都是统计独立的，并提供了过渡路径的代表性样本。该方法在一维四次振荡器上进行了说明。
