On the structure of the active Fokker-Planck equation

Recently, it has been experimentally discovered, and theoretically proved, that the stationary velocity distribution function of a non-interactive active stochastic system is bimodal. In this work, we theoretically reveal the condition under which a bimodal distribution will arise, and the condition under which this bimodal distribution will become Gaussian. This condition depends 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.