Driven tracer dynamics in a one dimensional quiescent bath

The dynamics of a driven tracer in a quiescent bath subject to geometric confinement models a broad range of phenomena. We explore this dynamics in a 1D lattice model, where geometric confinement is tuned by varying the rate of particle overtaking. Previous studies of the model's stationary properties on a ring of L sites have revealed a phase in which the bath density profile extends over an $\sim O\left(L\right)$ distance from the tracer and the tracer's velocity vanishes as ∼1/L. Here, we study the model's long time dynamics in this phase for L → ∞. We show that the bath density profile evolves on a $\sim \sqrt{t}$ time-scale and, correspondingly, that the tracer's velocity decays as $\sim 1/\sqrt{t}$. Unlike the well-studied case of a non-driven tracer, whose dynamics becomes diffusive whenever overtaking is allowed, we here find that driving the tracer preserves its hallmark sub-diffusive single-file dynamics, even in the presence of overtaking. (paper)