We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic timescale $D_R^{-1}$ set by the rotational diffusion constant $D_R$. We show that, at short times $t\ll D_R^{-1}$, the presence of “activeness” results in a strongly anisotropic and nondiffusive dynamics in the $\left(xy\right)$ plane. We compute exactly the marginal distributions of the $x$ and $y$ position coordinates along with the radial distribution, which are all shown to be non-Brownian. In addition, we show that, at early times, the ABP has anomalous first-passage properties, characterized by non-Brownian exponents.

• Received 27 April 2018
• Revised 20 July 2018

DOI:https://doi.org/10.1103/PhysRevE.98.062121