Active Brownian Motion in two-dimensions under Stochastic Resetting

Abstract: We study the position distribution of an active Brownian particle (ABP) in the presence of stochastic resetting in two spatial dimensions. We consider three different resetting protocols : (I) where both position and orientation of the particle are reset, (II) where only the position is reset, and (III) where only the orientation is reset with a certain rate $r.$ We show that in the first two cases the ABP reaches a stationary state. Using a renewal approach, we calculate exactly the stationary marginal position distributions in the limiting cases when the resetting rate $r$ is much larger or much smaller than the rotational diffusion constant $D_R$ of the ABP. We find that, in some cases, for a large resetting rate, the position distribution diverges near the resetting point; the nature of the divergence depends on the specific protocol. For the orientation resetting, there is no stationary state, but the motion changes from a ballistic one at short-times to a diffusive one at late times. We characterize the short-time non-Gaussian marginal position distributions using a perturbative approach.