Memory effects and active Brownian diffusion

TL;DR

This paper investigates how finite-time correlations in the orientation dynamics of active Brownian particles influence their diffusivity, proposing models with correlated environmental fluctuations and damping effects to predict changes in diffusion behavior.

Contribution

It introduces and analyzes two models incorporating memory effects in the propulsion dynamics of microswimmers, highlighting their impact on diffusivity.

Findings

Correlated environmental fluctuations can enhance diffusivity.

Damped propulsion fluctuations can suppress diffusivity.

Memory effects significantly influence active particle diffusion.

Abstract

A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer's diffusivity. To this purpose we propose and solve two alternative models. In the first one we simply assume that the environmental fluctuations governing the swimmer's propulsion are exponentially correlated in time, whereas in the second one we account for possible damped fluctuations of the propulsion velocity around the swimmer's axis. The corresponding swimmer's diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.