  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.
