# A new approach in an analytical method for diffusion dynamics for the presence of delocalized sink in a potential well: Application to different potential curves

## TL;DR

This paper introduces a novel analytical approach to solve the one-dimensional Fokker-Planck equation with delocalized sinks, simplifying calculations of rate constants across various potential energy curves.

## Contribution

The authors present a new method that avoids matrix equation solutions for rate constants, applicable to multiple potential energy profiles.

## Key findings

- Method successfully applied to flat, linear, and parabolic potentials.
- Simplifies calculation process compared to previous matrix-based methods.
- Provides analytical solutions in the Laplace domain for diffusion with delocalized sinks.

## Abstract

We provide a new approach to solve one dimension Fokker-Planck equation in the Laplace domain for the case where a particle is evolving in a potential energy curve in the presence of general delocalized sink. We also calculate rate constants in the presence of non-localized sink on different potential energy curves. In the previous method, we need to solve matrix equations to calculate rate constant but in our method, it is not required. We also calculate the rate constant by using the method to some known potential curve, viz, flat potential, linear potential, and parabolic potential.