Encounter-based approach to diffusion with resetting

TL;DR

This paper explores how stochastic resetting affects diffusion-controlled reactions using an encounter-based approach, revealing that boundary local time resetting can influence surface reaction mechanisms without altering the fundamental propagator.

Contribution

It introduces the concept of boundary local time resetting and analyzes its effects on diffusion-reaction processes, providing new insights into reaction mechanisms under resetting conditions.

Findings

Position resetting affects the propagator and related quantities.

Boundary local time resetting does not change the conventional propagator.

Surface reaction mechanisms can be significantly influenced by local time resetting.

Abstract

An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we investigate the effects of stochastic resetting onto diffusion-controlled reactions in bounded confining domains. We first discuss the effect of position resetting onto the propagator and related quantities; in this way, we retrieve a number of earlier results but also provide complementary insights onto them. Second, we introduce boundary local time resetting and investigate its impact. Curiously, we find that this type of resetting does not alter the conventional propagator governing the diffusive dynamics in the presence of a partially reactive target with a constant reactivity. In turn, the generalized propagator for other surface reaction mechanisms can be significantly affected. Our general results are illustrated for diffusion on an interval with reactive endpoints. Further perspectives and some open problems are discussed.