Lateral diffusion on a frozen random surface

TL;DR

This paper derives an exact expression for the lateral diffusion coefficient of a Brownian particle on a static, uncorrelated random surface, providing bounds and insights into diffusion behavior on complex geometries.

Contribution

It presents an exact calculation of the lateral diffusion coefficient for particles on a quenched, uncorrelated random surface, advancing understanding of diffusion in disordered environments.

Findings

The diffusion coefficient is bounded between known limits.

Exact mean square displacement is derived for uncorrelated surfaces.

The results clarify diffusion behavior on static random surfaces.

Abstract

The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a Brownian particle on a fluctuating surface, which has been derived by Naji and Brown. The mean square displacement of the particle projected on a base plane is calculated exactly under the condition that the surface with a constant shape has no spatial correlation. We prove that the obtained lateral diffusion coefficient is in between the known upper and lower bounds.