Anisotropic Brownian particles under resetting

Abstract

We study analytically the dynamics of an anisotropic particle subjected to different stochastic resetting schemes in two dimensions. The Brownian motion of shape-asymmetric particles in two dimensions results in anisotropic diffusion at short times, while the late-time transport is isotropic due to rotational diffusion. We show that the presence of orientational resetting promotes the anisotropy to late times. When the spatial and orientational degrees of freedom are reset, we find that a non-trivial spatial probability distribution emerges in the steady state that is determined by the initial orientation, particle asymmetry and the resetting rate. When only spatial degrees of freedom are reset while the orientational degree of freedom is allowed to evolve freely, the steady state is independent of the particle asymmetry. When only particle orientation is reset, the late-time probability density is given by a Gaussian with an effective diffusion tensor, including off-diagonal terms, determined by the resetting rate. Generally, the coupling between the translational and rotational degrees of freedom, when combined with stochastic resetting, gives rise to unique behaviour at late times not present in the case of symmetric particles. Considering recent developments in experimental implementations of resetting, our results can be useful for the control of asymmetric colloids, for example in self-assembly processes.