Driven tracer in the Symmetric Exclusion Process: linear response and beyond

Aurélien Grabsch, Pierre Rizkallah, Pierre Illien, Olivier Bénichou

Published 2022-07-26Version 1

Tracer dynamics in the Symmetric Exclusion Process (SEP), where hardcore particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by some external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference, and higher-order moments but only in the high-density limit. Here, we provide a general hydrodynamic framework that allows us to determine the first cumulants of bath-tracer correlations and of the tracer position at linear order in the driving and at arbitrary density. We also go beyond linear response by determining the second cumulant and the corresponding density profile at quadratic order in the driving