Chirality Reversing Active Brownian Motion in Two Dimensions

Abstract

We study the dynamics of a chirality reversing active Brownian particle, which models the chirality reversing active motion common in many microorganisms and microswimmers. We show that, for such a motion, the presence of the two time-scales set by the chirality reversing rate $\gamma$ and rotational diffusion constant $D_R$ gives rise to four dynamical regimes, namely, (I) $t \ll \text{min}(\gamma^{-1}, D_R^{-1})$, (II) $\gamma^{-1} \ll t \ll D_R^{-1}$, (III) $D_R^{-1} \ll t \ll \gamma^{-1}$ and (IV) $t \gg \text{max}(\gamma^{-1}, D_R^{-1})$, each showing different behaviour. The short-time regime (I) is characterized by a strongly anisotropic and non-Gaussian position distribution, which crosses over to a diffusive Gaussian behaviour in the long-time regime (IV) via an intermediate regime (II) or (III), depending on the relative strength of $\gamma$ and $D_R$. In regime (II), the chirality reversing active Brownian motion reduces to that of an ordinary active Brownian particle, with an effective rotation diffusion coefficient which depends on the angular velocity. Finally, we find that, the regime (III) is characterized by an effective chiral active Brownian motion.