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We study the problem of the computation of the effective diffusion constantof a Brownian particle diffusing in a random potential which is given by afunction $V(\phi)$ of a Gaussian field $\phi$. A self similar renormalizationgroup analysis is applied to a mathematically related problem of the effectivepermeability of a random porous medium from which the diffusion constant of therandom potential problem can be extracted. This renormalization group approachreproduces practically all known exact results in one and two dimensions. Theresults are confronted with numerical simulations and we find that theiraccuracy is good up to points well beyond the expected perturbative regime. Theresults obtained are also tentatively applied to interacting particle systemswithout disorder and we obtain expressions for the self-diffusion constant interms of the excess thermodynamic entropy. This result is of a form that hascommonly been used to fit the self diffusion constant in molecular dynamicssimulations.

Self Similar Renormalization Group Applied to Diffusion in non-Gaussian Potentials