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arXiv · 2405.00654

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

Kapil Sharma·Soumyabrata Saha·Sandeep Jangid·Tridib Sadhu
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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.

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Kapil Sharma, Soumyabrata Saha, Sandeep Jangid, Tridib Sadhu. 2025-12-02. Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond. https://doi.org/10.1103/dzf3-8wpt

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