ON THE STRUCTURE OF THE ACTIVE FOKKER-PLANCK EQUATION

Recently, it has been experimentally discovered, and analytically proved, that the stationary velocity distribution function of an active ideal gas is bimodal. In this work, we analytically reveal the condition under which a bimodal velocity distribution arises, and the condition under which this bimodal distribution will become Gaussian. This condition is seen to depend on two important time scales in the problem, namely, reorientation and inertial time scales. Briefly, when the inertial time is larger than the orientation time, the active Fokker-Planck stationary solution admits a bimodal structure. The inverse condition is seen to admit a Gaussian structure.