First Passage Resetting Gas

TL;DR

This paper analyzes a one-dimensional gas of Brownian particles with a reset mechanism at a fixed threshold, revealing a solvable non-equilibrium stationary state with strong correlations and exact observable calculations.

Contribution

It introduces a model of reset Brownian particles with an exact solution for the non-equilibrium stationary state and its physical observables.

Findings

The system reaches a non-equilibrium stationary state with strong correlations.

Exact expressions for density profiles and particle distributions are derived.

The model exhibits long-range correlations emerging purely from dynamics.

Abstract

We study a one-dimensional gas of $N$ Brownian particles that diffuse independently but are simultaneously reset whenever any of them reaches a fixed threshold located at $L > 0$. For any $N > 2$, the system reaches a non-equilibrium stationary state (NESS) at long-times with strong long-range correlations. These correlations emerge purely from the dynamics, and not from built-in interactions. Despite being strongly correlated, the NESS has a solvable structure that allows for an exact computation of several physical observables, both global and local. These include the average density profile, the distribution of the position of the $k$-th ordered particles, the distribution of the gap between two consecutive particles and the full counting statistics, i.e., the distribution of the number of particles in a finite interval around the origin.