Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond

TL;DR

This paper develops a hydrodynamic framework to analyze the behavior of a driven tracer particle in the symmetric exclusion process, extending understanding beyond linear response and providing the first bias-dependent variance results for arbitrary densities.

Contribution

It introduces a general hydrodynamic approach to compute the first cumulants of tracer dynamics under external driving forces in the SEP, including the bias dependence of the variance for any density.

Findings

First bias-dependent variance of a driven tracer in SEP for arbitrary density

Hydrodynamic framework applicable beyond SEP to other 1D driven obstacle configurations

Extension of analytical results beyond high-density limit and linear response

Abstract

Tracer dynamics in the Symmetric Exclusion Process, 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 an 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 the bath-tracer correlations and of the tracer's position in function of the driving force, up to quadratic order (beyond linear response). This result constitutes the first determination of the bias-dependence of the variance of a driven tracer in the SEP for an arbitrary density. The framework presented here can be applied, beyond the SEP, to more general configurations of a driven tracer in interaction with obstacles in one dimension.