Perturbation theory for the effective diffusion constant in a medium of random scatterer

Abstract

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.

22 pages, 6 figures, IOP (J. Phys. A. style)

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• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Renormalization of Drift and Diffusivity in Random Gradient Flows
• Continuum Derrida Approach to Drift and Diffusivity in Random Media
• The Effect of Helicity on the Effective Diffusivity for Incompressible Random Flows
• Effective diffusion constant in a two dimensional medium of charged point scatterers

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• Distance traveled by random walkers before absorption in a random medium
• Improved field theoretical approach to noninteracting Brownian particles in a quenched random potential