Active Brownian motion with directional reversals

Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a two dimensions, the presence of timescales set by rotational diffusion constant ${D}_{R}$ reversal rate $\ensuremath{\gamma}$ gives rise to four distinct dynamical regimes: (I) $t\ensuremath{\ll}min({\ensuremath{\gamma}}^{\ensuremath{-}1},{D}_{R}^{\ensuremath{-}1}),$ (II) ${\ensuremath{\gamma}}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{D}_{R}^{\ensuremath{-}1}$, (III) ${D}_{R}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\gamma}}^{\ensuremath{-}1}$, (IV) $t\ensuremath{\gg}max({\ensuremath{\gamma}}^{\ensuremath{-}1}, {D}_{R}^{\ensuremath{-}1})$, showing behaviors. characterize these behaviors analytically computing position distribution persistence exponents. The shows crossover from strongly nondiffusive anisotropic behavior at short times diffusive isotropic via an intermediate regime, II or III. In regime II, we along orthogonal initial orientation function scaled variable $z\ensuremath{\propto}{x}_{\ensuremath{\perp}}/t$ nontrivial scaling function, $f(z)={(2{\ensuremath{\pi}}^{3})}^{\ensuremath{-}1/2}\mathrm{\ensuremath{\Gamma}}(1/4+iz)\mathrm{\ensuremath{\Gamma}}(1/4\ensuremath{-}iz)$. Furthermore, exact first-passage time distribution, that exponent $\ensuremath{\alpha}=1$ emerges due this regime.