Run-and-tumble particles in two dimensions under stochastic resetting conditions

Abstract

We study the effect of stochastic resetting on a run-and-tumble particle (RTP) in two spatial dimensions. We consider a resetting protocol which affects both the position and orientation of the RTP: the particle undergoes constant-rate positional resetting to a fixed point in space and a random orientation. We compute the radial and x-marginal stationary-state distributions and show that while the former approaches a constant value as r → 0, the latter diverges logarithmically as x → 0. On the other hand, both the marginal distributions decay exponentially with the same exponent when they are far from the origin. We also study the temporal relaxation of the RTP and show that the positional distribution undergoes a dynamic transition to a stationary state. We also study the first-passage properties of the RTP in the presence of resetting and show that the optimization of the resetting rate can minimize the mean first-passage time. We also provide a brief discussion of the stationary states for resetting a particle to an initial position with a fixed orientation.