Tuning the strength of emergent correlations in a Brownian gas via batch resetting

TL;DR

This paper investigates how batch resetting in a Brownian gas influences long-range correlations, revealing a tunable nonequilibrium stationary state with a phase transition at a critical particle number.

Contribution

It provides exact analytical results for correlations in a resetting Brownian gas, showing how correlation strength can be tuned and identifying a phase transition at a critical particle number.

Findings

Correlations exhibit non-monotonic time dependence for 1<m<N.

Stationary correlation strength can be tuned by m.

A phase transition occurs at N=6, independent of spatial dimension.

Abstract

We study a gas of $N$ diffusing particles on the line subject to batch resetting: at rate $r$, a uniformly random subset of $m$ particles is reset to the origin. Despite the absence of interactions, the dynamics generates a nonequilibrium stationary state (NESS) with long-range correlations. We obtain exact results, both for the NESS and for the time dependence of the correlations, which are valid for arbitrary $m$ and $N$. By varying $m$, the system interpolates between an uncorrelated regime ($m=1$) and the fully synchronous resetting case ($m=N$). For all $1<m<N$, correlations exhibit a non-monotonic time dependence due to the emergence of an intrinsic decorrelation mechanism. In the stationary state, the correlation strength can be tuned by varying $m$, and it displays a transition at a critical value $N_c=6$. Our predictions extend straightforwardly to any spatial dimension $d$ and the critical value $N_c=6$ remains the same in all dimensions. Our predictions are testable in existing experimental setups on optically trapped colloidal particles.