Effect of Partial Absorption on Diffusion with Resetting

TL;DR

This paper investigates how partial absorption affects the search efficiency of diffusive particles with stochastic resetting, revealing that absorption velocity influences mean absorption time and survival probabilities in single and multi-particle systems.

Contribution

It introduces a detailed analysis of partial absorption effects on diffusion with resetting, extending to multiparticle systems and quantifying changes in survival probabilities.

Findings

Mean time to absorption increases with partial absorption, proportional to 1/a.

Average survival probability is modified by a factor depending on 1/a.

Decay rate of typical survival probability decreases with partial absorption, proportional to 1/a.

Abstract

The effect of partial absorption on a diffusive particle which stochastically resets its position with a finite rate $r$ is considered. The particle is absorbed by a target at the origin with absorption `velocity' $a$; as the velocity $a$ approaches $\infty$ the absorption property of the target approaches that of a perfectly-absorbing target. The effect of partial absorption on first-passage time problems is studied, in particular, it is shown that the mean time to absorption (MTA) is increased by an additive term proportional to $1/a$. The results are extended to multiparticle systems where independent searchers, initially uniformly distributed with a given density, look for a single immobile target. It is found that the average survival probability $P^{av}$ is modified by a multiplicative factor which is a function of $1/a$, whereas the decay rate of the typical survival probability $P^{typ}$ is decreased by an additive term proportional to $1/a$.