Dynamics of Run-and-Tumble Particles in Dense Single-File Systems

TL;DR

This paper models the movement of run-and-tumble particles in crowded single-file environments, deriving exact distributions and revealing how crowding influences their anomalous subdiffusive behavior over time.

Contribution

It extends classical exclusion process models to include run-and-tumble dynamics and provides exact analytical results for particle displacement distributions in high-density settings.

Findings

Cumulants of particle position increase with tumbling probability at intermediate times.

Long-time behavior shows subdiffusive scaling proportional to √n, independent of tumbling.

Analytical results facilitate comparison with experimental microswimmer trajectories.

Abstract

We study a minimal model of self-propelled particle in a crowded single-file environment. We extend classical models of exclusion processes (previously analyzed for diffusive and driven tracer particles) to the case where the tracer particle is a run-and-tumble particle (RTP), while all bath particles perform symmetric random walks. In the limit of high density of bath particles, we derive exact expressions for the full distribution $\mathcal{P}_n(X)$ of the RTP position $X$ and all its cumulants, valid for arbitrary values of the tumbling probability $\alpha$ and time $n$. Our results highlight striking effects of crowding on the dynamics: even cumulants of the RTP position are increasing functions of $\alpha$ at intermediate timescales, and display a subdiffusive anomalous scaling $\propto \sqrt{n}$ independent of $\alpha$ in the limit of long times $n\to \infty$. These analytical results set the ground for a quantitative analysis of experimental trajectories of real biological or artificial microswimmers in extreme confinement.