Extreme statistics and spacing distribution in a Brownian gas correlated by resetting

TL;DR

This paper analyzes a one-dimensional Brownian gas with simultaneous resetting to the origin, deriving exact results for various observables in the non-equilibrium stationary state induced by resetting.

Contribution

It provides exact analytical expressions for density, particle position distributions, and spacing in a resetting Brownian gas, revealing long-range correlations.

Findings

Exact density and spacing distributions derived

Confirmation of analytical results through simulations

Discussion of potential experimental realization

Abstract

We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are {\it simultaneously} reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range interactions induced by the simultaneous resetting. Despite the presence of strong correlations, we show that several observables can be computed exactly, which include the global average density, the distribution of the position of the $k$-th rightmost particle and the spacing distribution between two successive particles. Our analytical results are confirmed by numerical simulations. We also discuss a possible experimental realisation of this resetting gas using optical traps.