# Ramifications of disorder on active particles in one dimension

## TL;DR

This paper investigates how quenched disorder affects the behavior of active run-and-tumble particles in one dimension, revealing slow dynamics, diffusive motion, and strong clustering depending on the type of disorder and system size.

## Contribution

It provides a comprehensive analysis of disorder effects on active particles, including steady-state distributions, dynamics, and clustering in many-particle systems, highlighting new phenomena.

## Key findings

- Disordered potential causes logarithmically slow diffusion similar to equilibrium particles.
- Disorder in speed or tumbling rate generally leads to diffusive motion, with possible anomalous diffusion.
- Disorder in the potential induces strong clustering with mean cluster size scaling with system size.

## Abstract

The effects of quenched disorder on a single and many active run-and-tumble particles is studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to non-disordered systems.