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We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic timescale Dₑ^-1 set by the rotational diffusion constant Dₑ. We show that, at short times tDₑ^-1, the presence of ``activeness'' results in a strongly anisotropic and nondiffusive dynamics in the (xy) 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.
Basu et al. (Fri,) studied this question.
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