Extreme Statistics and Spacing Distribution in a Brownian Gas Correlated by Resetting

We study a one-dimensional gas of N Brownian particles that diffuse independently, but are simultaneously reset to the origin at a constant rate r. The system approaches a nonequilibrium stationary state 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 kth rightmost particle, and the spacing distribution between two successive particles. Our analytical results are confirmed by numerical simulations. We also discuss a possible experimental realization of this resetting gas using optical traps.

Automated summary

In this study, we investigate a one-dimensional gas of N Brownian particles that are reset simultaneously. Despite the presence of strong correlations, we find that several observables, such as the global average density and the distributions of particle positions and spacings, can be computed exactly. Our findings are confirmed by numerical simulations and we also discuss the potential experimental realization of this resetting gas using optical traps.