运用CTRW-Metropolis模型数值研究亚稳势中粒子逃逸问题

基于连续时间随机行走(CTRW)理论,实现反常扩散条件下对跳跃步长和等待时间分布函数的抽样,改进Metropolis抽样判定方法以适用于存在非线性势的情况.数值研究布朗粒子在亚稳势下的逃逸速率.结果显示,稳定逃逸速率γ_st随反常指数α非单调变化,在超扩散条件下存在极大值和位垒相消现象.     

Diffusion with random traps: Transient one-dimensional kinetics in a linear potential

The problem of one-dimensional diffusion with random traps is solved without and with a constant field of force. Using an eigenvalue expansion for long times and the method of images for short times we give an exact, straightforward solution for the time dependence of the mean survival probability and the mean probability density for returning to the origin. Using the backward equation approach, we determine the mean survival time and the mean residence time density at the origin. We comment on the relation between these solutions and those for one-dimensional diffusion with random reflectors.