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

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.

arXiv comment6 pages, 4 figures

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Cited by in corpus (13)

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• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
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