Diffusion in a model for active Brownian motion

Due to their small mass, microorganisms whose sizes are of the order of the microns, such as marine bacteria, are continuously buffeted by Brownian forces, which can substantially affect their motion. Here we extend the analysis of a model recently introduced to describe the dynamics of a microorganism moving under the combined influences of its own propulsion system and of Brownian forces. In the high dissipation regime, the nature of the motion is determined by a synergy between these two contributions. Although the motion can be extremely directional over short time scales, it is always diffusive when observed over long times.