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

Abstract

We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(\varphi )$ of a Gaussian field $\varphi$. A self similar renormalization group analysis is applied to a mathematically related problem of the effective permeability of a random porous medium from which the diffusion constant of the random potential problem can be extracted. This renormalization group approach reproduces practically all known exact results in one and two dimensions. The results are confronted with numerical simulations and we find that their accuracy is good up to points well beyond the expected perturbative regime. The results obtained are also tentatively applied to interacting particle systems without disorder and we obtain expressions for the self-diffusion constant in terms of the excess thermodynamic entropy. This result is of a form that has commonly been used to fit the self diffusion constant in molecular dynamics simulations.

14 pages, 3 .eps figures, IOP style file

References in corpus (6)

• Dynamical transition for a particle in a squared Gaussian potential
• Self diffusion in a system of interacting Langevin particles
• Continuum Derrida Approach to Drift and Diffusivity in Random Media
• Perturbation theory for the effective diffusion constant in a medium of random scatterer
• Effective diffusion constant in a two dimensional medium of charged point scatterers
• Effective drift and diffusivity in non-Gaussian random gradient flows

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