Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
J Chem Phys. 2012 Feb 21;136(7):074506. doi: 10.1063/1.3685418.
We present a method, founded on previous renewal approaches as the classical Wilemski-Fixman approximation, to describe the escape dynamics from a potential well of a particle subject to non-Markovian fluctuations. In particular, we show how to provide an approximated expression for the distribution of escape times if the system is governed by a generalized Langevin equation (GLE). While we show that the method could apply to any friction kernel in the GLE, we focus here on the case of power-law kernels, for which extensive literature has appeared in the last years. The method presented (termed as two-point approximation) is able to fit the distribution of escape times adequately for low potential barriers, even if conditions are far from Markovian. In addition, it confirms that non-exponential decays arise when a power-law friction kernel is considered (in agreement with related works published recently), which questions the existence of a characteristic reaction rate in such situations.
我们提出了一种方法，该方法基于先前的更新方法，如经典的 Wilemski-Fixman 逼近方法，用于描述非马尔可夫涨落作用下粒子从势阱中逃逸的动力学。特别是，我们展示了如何在系统受广义朗之万方程（GLE）控制的情况下，给出逃逸时间分布的近似表达式。虽然我们表明该方法可以应用于 GLE 中的任何摩擦核，但我们在此重点关注幂律核的情况，近年来已经有大量相关文献对此进行了研究。所提出的方法（称为两点逼近）能够适当地拟合逃逸时间的分布，即使在远离马尔可夫的情况下，对于低势垒也是如此。此外，它证实了当考虑幂律摩擦核时会出现非指数衰减（与最近发表的相关工作一致），这使得在这种情况下存在特征反应速率的问题受到质疑。
