# Reaction-Diffusion dynamics in presence of active barrier: Pinhole sink

## TL;DR

This paper derives a semi-analytic expression for the survival probability of particles diffusing in an active potential well with a sink, addressing a gap where no analytic solutions previously existed, and elucidates physical insights.

## Contribution

It provides the first semi-analytic solution for survival probability in a system with an active barrier and localized sink, overcoming the challenge of inverse Laplace transform.

## Key findings

- Derived semi-analytic expression for survival probability
- Explained physical aspects of diffusion in active potential wells
- Addressed a gap in analytical solutions for such systems

## Abstract

In this article, we give a semi-analytic expression for survival probability when particles are diffusing in an active potential well. There is no analytic solution available in the literature, due to the requirement of inverse Laplace transform of the propagator, when a sink is placed at the uphill of the parabolic potential even in case of the localized sink. We also explain some of the physical aspects by using our solution.