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

TL;DR

This paper applies a self-similar renormalization group method to compute the effective diffusion constant of particles in non-Gaussian random potentials, achieving accurate results beyond perturbative regimes and connecting to interacting particle systems.

Contribution

It introduces a renormalization group approach for non-Gaussian potentials and demonstrates its effectiveness in predicting diffusion constants in complex systems.

Findings

Reproduces known results in 1D and 2D

Accurately predicts diffusion constants beyond perturbative limits

Links self-diffusion to thermodynamic entropy in interacting systems

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 $V(\phi)$ of a Gaussian field $\phi$. 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.