Diffusion on a flat potential with a new localized sink: Exact Analytical Solution

TL;DR

This paper presents an exact analytical method for solving diffusion problems with a localized sink in a flat potential, applicable to other potentials, using the Laplace transform of Green's functions.

Contribution

It introduces a novel analytical approach for solving the Smoluchowski equation with a localized sink in flat and other potentials.

Findings

Exact solutions for diffusion with localized sink

Method applicable to various potentials

Utilizes Laplace transform of Green's function

Abstract

We give a method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion in a flat potential in the presence of a new localized sink. The Diffusive motion is described using the Smoluchowski equation. Our method requires the knowledge of Laplace transform of Green's function for the motion in absence of the sink. The same model for sink can be used to deal with other potentials.