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 α and time n . Our results highlight striking effects of crowding on the dynamics: even cumulants of the RTP position are increasing functions of α at intermediate timescales, and display a subdiffusive anomalous scaling $\propto \sqrt{n}$ independent of α 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.

Keywords

• active matter
• run-and-tumble motion
• lattice models in statistical physics