Driven tracer dynamics in a one dimensional quiescent bath

TL;DR

This paper investigates the long-time driven tracer dynamics in a 1D lattice model with geometric confinement, revealing sub-diffusive behavior persists despite overtaking, with bath density evolving as sqrt(t) and tracer velocity decaying as 1/sqrt(t).

Contribution

It demonstrates that driving a tracer in a confined 1D bath maintains sub-diffusive dynamics even when overtaking is possible, extending understanding of tracer behavior in such systems.

Findings

Bath density profile evolves as sqrt(t) over time.

Tracer velocity decays as 1/sqrt(t).

Sub-diffusive dynamics persist despite overtaking.

Abstract

The dynamics of a driven tracer in a quiescent bath subject to geometric confinement effectively models a broad range of phenomena. We explore this dynamics in a 1D lattice model where geometric confinement is tuned by varying particle overtaking rates. 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 $\sim \mathcal{O}(L)$ distance from the tracer and the tracer's velocity vanishes as $\sim 1/L$. Here, we study the model's dynamics in this phase as $L\rightarrow \infty$ and for long times. 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 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.