Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement

TL;DR

This paper analytically investigates the short-time behavior of the mean-square displacement of active Brownian and inertial particles in disordered environments, revealing ballistic and superballistic regimes and confirming results with simulations and potential experiments.

Contribution

It provides a systematic short-time expansion of the MSD for active particles in disordered landscapes, including inertial effects, which is a novel analytical approach.

Findings

Disorder induces ballistic behavior in overdamped particles.

Inertial particles exhibit superballistic regimes with MSD scaling as t^3 and t^4.

Theoretical predictions are confirmed by computer simulations and are experimentally verifiable.

Abstract

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is $\alpha=3$ and $\alpha=4$. We confirm our theoretical predictions by computer simulations. Moreover they are verifiable in experiments on self-propelled colloids in random environments.