Semi-infinite simple exclusion process: from current fluctuations to target survival

TL;DR

This paper derives the full current fluctuation statistics for a semi-infinite symmetric exclusion process connected to a reservoir, addressing open problems related to target survival and particle injection statistics.

Contribution

It provides the first exact cumulant generating function for current in a semi-infinite SEP, extending understanding beyond finite and infinite geometries.

Findings

Derived the full cumulant generating function of the current.

Solved the target survival probability problem.

Analyzed the statistics of particles injected by a localized source.

Abstract

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but so far most results are restricted to two geometries: (i) a finite system between two reservoirs, which does not conserve the number of particles but reaches a nonequilibrium steady state, and (ii) an infinite system which conserves the number of particles but never reaches a steady state. Here, we determine the full cumulant generating function of the integrated current in the important intermediate situation of a semi-infinite system connected to a reservoir, which does not conserve the number of particles and never reaches a steady state. This result is obtained thanks to the determination of the full spatial structure of the correlations which remarkably obey the very same closed equation recently obtained in the infinite geometry. Besides their intrinsic interest, these results allow us to solve two open problems: the survival probability of a fixed target in the SEP, and the statistics of the number of particles injected by a localized source.