Active Brownian Motion in Two Dimensions

TL;DR

This paper analyzes the short-time dynamics of a single active Brownian particle in two dimensions, revealing anisotropic, non-diffusive behavior and anomalous first-passage properties due to activity.

Contribution

It provides exact calculations of position distributions and characterizes early-time anomalous first-passage behavior of active Brownian particles.

Findings

Short-time dynamics are anisotropic and non-diffusive.

Exact marginal and radial distributions are non-Brownian.

Early-time first-passage exhibits anomalous exponents.

Abstract

We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion constant $D_R$. We show that, at short-times $t \ll D_R^{-1}$, the presence of `activness' results in a strongly anisotropic and non-diffusive 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.