Diffusion with Local Resetting and Exclusion

TL;DR

This paper investigates how local resetting affects interacting many-body systems, specifically diffusing particles with exclusion, using a mean-field approach validated by simulations to understand the complex interplay between interactions and resetting.

Contribution

It introduces a mean-field framework to analyze local resetting in many-body systems, extending beyond the traditional renewal approach applicable to global resetting.

Findings

Mean-field approach effectively describes local resetting in interacting particles.

Numerical simulations confirm the validity of the mean-field results.

Reveals complex interactions between resetting mechanisms and particle exclusion.

Abstract

Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in interacting many-body systems, even the simplest scenarios involving resetting give rise to the notion of local resetting, whose analysis falls outside the scope of the renewal approach. A prime example is that of diffusing particles with excluded volume interactions that independently attempt to reset their position to the origin of a 1D lattice. With renewal rendered ineffective, we instead employ a mean-field approach whose validity is corroborated via extensive numerical simulations. The emerging picture sheds first light on the non-trivial interplay between interactions and resetting in many-body systems.