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Classical diffusion in strong random media
Authors:Michael W Deem  David Chandler
Institution:(1) Department of Chemical Engineering, University of California, 94720 Berkeley, California;(2) Department of Chemistry, University of California, 94720 Berkeley, California
Abstract:We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.
Keywords:Diffusion  random media  functional integral  perturbation theory  renormalization group
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