First Passage Resetting Gas

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.

7 pages, 2 figures, slightly revised version before submission