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

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• Nonequilibrium statistical mechanics
• Stochastic processes
• Active Brownian particles
• Living matter & active matter
• Self-propelled particles
• Fokker–Planck equation
• Stochastic differential equations