Mobility Anisotropy Reshapes Self-Propelled Motion

We exactly solve the nonequilibrium dynamics of a harmonically trapped self-propelled particle with anisotropic translational mobility in two dimensions, relevant to rodlike microswimmers and wheeled robots. The mean displacement and MSD reveal a quasi-steady plateau with vanishing fluctuations in the high-persistence regime. An exact calculation of steady-state fourth moment yields a negative excess kurtosis that varies non-monotonically with the ratio of mechanical to rotational relaxation timescales. This gives rise to a strictly sub-Gaussian steady-state position distribution, in which the particle with anisotropic mobility, in high persistence regime, is displaced into the high-potential region lying outside the stationary contour set by the activity and harmonic confinement. This is further corroborated by the relaxation of the MSD from the quasi-steady plateau to the steady-state regime.