Long-time tail effects on particle diffusion in a disordered system

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Abstract
We present a simple formulation of an effective-medium approximation to a model of particle transport in a random medium. The small- and large-time asymptotic properties of the effective transition rate in one dimension are computed. We also derive the first three corrections to the leading asymptotic terms in the expansion. The results for the mean-square displacement and fourth moment are in excellent agreement with a Monte Carlo simulation.