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

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.