Asymmetric Random Walk in a One-Dimensional Multizone Environment
We consider a random walk model in a one-dimensional environment formed by several zones of finite widths with fixed transition probabilities. It is assumed that the transitions to the left and right neighboring points have unequal probabilities. In the continuous limit, we derive analytically the probability distribution function, which is mainly determined by a walker diffusion and a drift and takes perturbatively the interface effects between zones into account. It is used for computing the probability to find a walker at a given space-time point and the time dependence of the mean squared displacement of a walker trajectory, which reveals the transient anomalous diffusion. To justify our approach, the probability function is compared with the results of numerical simulations for the case of three-zone environment.
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