Active transport in dense diffusive single-file systems

TL;DR

This paper analyzes a minimal model of active transport in crowded single-file systems, deriving explicit distributions and cumulants of the tracer particle's position, revealing anomalous scaling and Gaussian convergence despite asymmetries.

Contribution

It provides the full statistical description of active tracer dynamics in dense single-file environments, extending classical models to include bias and activity.

Findings

Cumulants scale as √n, indicating anomalous diffusion.

Cumulants of same parity are equal, characteristic of Skellam distribution.

Distribution converges to Gaussian despite asymmetric density profiles.

Abstract

We study a minimal model of active transport in crowded single-file environments which generalises the emblematic model of single file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is biased by an external force, while all other particles of the environment (bath) perform unbiased diffusions. We derive explicit expressions, valid in the limit of high density of bath particles, of the full distribution $P_n(X)$ of the TP position and of all its cumulants, for arbitrary values of the bias $f$ and for any time $n$. Our analysis reveals striking features, such as the anomalous scaling $\propto\sqrt{n}$ of all cumulants, the equality of cumulants of the same parity characteristic of a Skellam distribution and a convergence to a Gaussian distribution in spite of asymmetric density profiles of bath particles. Altogether, our results provide the full statistics of the TP position, and set the basis for a refined analysis of real trajectories of active particles in crowded single-file environments.