Search of stochastically gated targets with diffusive particles under resetting

TL;DR

This paper investigates how Poissonian resetting affects the reaction time of diffusive particles to stochastically gated targets, revealing optimal resetting rates and the impact of target dynamics on fluctuations.

Contribution

It introduces a model for diffusive search with stochastically gated targets under resetting and analyzes the conditions for optimal search times and fluctuation behaviors.

Findings

Optimal resetting rate depends on target transition rates.

System reduces to a partially absorbing boundary in certain limits.

Fluctuation behavior deviates from universal patterns due to target dynamics.

Abstract

The effects of Poissonian resetting at a constant rate $r$ on the reaction time between a Brownian particle and a stochastically gated target are studied. The target switches between a reactive state and a non-reactive one. We calculate the mean time at which the particle subject to resetting hits the target for the first time, while the latter is in the reactive state. The search time is minimum at a resetting rate that depends on the target transition rates. When the target relaxation rate is much larger than both the resetting rate and the inverse diffusion time, the system becomes equivalent to a partially absorbing boundary problem. In other cases, however, the optimal resetting rate can be a non-monotonic function of the target rates, a feature not observed in partial absorption. We compute the relative fluctuations of the first hitting time around its mean and compare our results with the ungated case. The usual universal behavior of these fluctuations for resetting processes at their optimum breaks down due to the target internal dynamics.