Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond

TL;DR

This paper derives an exact current fluctuation result for the symmetric simple exclusion process on a semi-infinite line, extending known results to this intermediate geometry and applying it to various complex scenarios.

Contribution

It provides the first exact current fluctuation result for the semi-infinite geometry using macroscopic fluctuation theory, confirmed by simulations.

Findings

Derived the current fluctuation result for semi-infinite line

Confirmed the result with rare event simulations

Applied the result to solve related complex problems

Abstract

Two influential exact results in classical one-dimensional diffusive transport are about current statistics for the symmetric simple exclusion process: one in the stationary state on a finite line coupled with two unequal reservoirs at the boundaries, and the other in the non-stationary state on an infinite line. We present the corresponding result for the intermediate geometry of a semi-infinite line coupled with a single reservoir. This result is obtained using the fluctuating hydrodynamics approach of macroscopic fluctuation theory and confirmed by rare event simulations using a cloning algorithm. We apply our exact result for solving several related challenging problems, namely, the full counting statistics in presence of a defect bond, exclusion process with localized injection, survival of a tagged particle in presence of an absorbing boundary, and the stretched exponential decay in a kinetically constrained model.