倾斜周期势下的连续时间无规行走

The Continuous Time Random Walk in the Tilted Periodic Field

连续时间无规行走(CTRW)是研究扩散问题的重要理论和方法。利用CTRW方法,通过解析推导和数值计算,在自由场中,分别模拟了正常扩散、欠扩散和超扩散三种情况下粒子的方均位移随着时间的变化;并进行对数线性拟合,数值计算得到的扩散系数与理论值相符。同时,在给出倾斜周期势下,自由粒子的扩散系数随参数F而变化,便观察到了反常扩散、局域化和弹道扩散。

Continuous time random walk （CTRW） is an important theory and method on diffusion. Based on the analytical derivation and numerical calculation, the mean square displacements of particles in the free field changing with time were showed in this paper including the normal diffusion, sub diffusion and super diffusion with CTRW. After log linear fitting on diffusion coefficients, the value of numerical calculation was consistent with theory. At the same time, the diffusion coefficients of the free particles in the tilted periodic potential are also discussed. The anomalous diffusion, localization and ballistic diffusion are observed with the change of the parameter F.