Abstract
We present an effective-medium approximation to a diffusion model of a particle in a one dimensional medium, that can be annihilated. This approximation is compared with results based on a multistate continuous-time random walk. The mean-square displacement and the annihilation rate in Laplace transformed form are computed in both schemes. We also analyse the small- and largetime asymptotic behavior of the effective hopping and annihilation probabilities per unit time. The effectivemedium approximation results are in full agreement with those of the multistate continuous-time random walk scheme only under a linear approximation of the square root that appears in the Green's function for a homogeneous medium.
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Pury, P.A., Prato, D.P. Diffusion and annihilation of a particle on a disordered chain. Z. Physik B - Condensed Matter 85, 117–121 (1991). https://doi.org/10.1007/BF01387796
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DOI: https://doi.org/10.1007/BF01387796