Effect of slow bonds on current fluctuations in the symmetric simple exclusion process

Abstract

The symmetric simple exclusion process (SSEP) is a paradigmatic model of classical non-equilibrium dynamics. Exact results for large deviations of particle current in the SSEP have been obtained in various settings using integrability-based methods. In this Article, we discuss how these results are modified in the presence of localized slow bonds. We consider three conventional geometries: (a) a finite one-dimensional lattice weakly coupled to unequal reservoirs at its boundaries, (b) a semi-infinite one-dimensional lattice weakly coupled to a boundary reservoir, and (c) an infinite one-dimensional lattice with localized slow bonds near the origin. For each case, we present exact expressions for the large deviation function of current and validate them through rare-event simulations based on the cloning algorithm. In connection with our results, we present an elementary derivation of the exact large deviation function for the current in the semi-infinite SSEP, complementing recent results obtained through more elaborate techniques.