Local resetting with geometric confinement

TL;DR

This paper investigates how local stochastic resetting of tracers affects the density profiles of interacting particles under geometric confinement, revealing phase transitions between different spatial arrangements.

Contribution

It introduces a mean-field framework for analyzing resetting in confined interacting particle systems and uncovers phase transitions driven by confinement and diffusivity ratios.

Findings

Resetting tracers create a tent-shaped density profile.

System exhibits a transition between particle expulsion and trapping states.

Mean-field approximation becomes exact at a critical point.

Abstract

"Local resetting" was recently introduced to describe stochastic resetting in interacting systems where particles independently try to reset to a common "origin". Our understanding of such systems, where the resetting process is itself affected by interactions, is still very limited. One ubiquitous constraint that is often imposed on the dynamics of interacting particles is geometric confinement, e.g. restricting rigid spherical particles to a channel so narrow that overtaking becomes difficult. We here explore the interplay between local resetting and geometric confinement in a system consisting of two species of diffusive particles: "bath" particles, and "tracers" which undergo local resetting. Mean-field analysis and numerical simulations show that the resetting tracers, whose stationary density profile exhibits a typical "tent-like" shape, imprint this shape onto the bath density profile. Upon varying the ratio of the degree of geometric confinement over particle diffusivity, the system is found to transition between two states. In one tracers expel bath particles away from the origin, while in the other they ensnare them instead. Between these two states, we find a special case where the mean field approximation becomes exact.