# Archive ouverte HAL – Active Brownian motion in two dimensions

### Urna Basu 1 Satya N. Majumdar 2 Alberto Rosso 2 Satya Majumdar 2 Gregory Schehr 2

#### Physical Review E , American Physical Society (APS), 2018, 98 (6), 〈10.1103/PhysRevE.98.062121〉

We study the dynamics of a single active Brownian particle (ABP) in a two-dimensional harmonic trap. The active particle has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion with diffusion constant $D_R$. The harmonic trap also induces a relaxational time-scale $\mu^{-1}$. We show that the competition between these two time scales leads to a nontrivial time evolution for the ABP. At short times a strongly anisotropic motion emerges leading to anomalous persistence/first-passage properties. At long-times, the stationary position distribution in the trap exhibits two different behaviours: a Gaussian peak at the origin in the strongly passive limit ($D_R \to \infty$) and a delocalised ring away from the origin in the opposite strongly active limit ($D_R \to 0$). The predicted stationary behaviours in these limits are in agreement with recent experimental observations.

• 1. Theoretical Condensed Matter Physics Division
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques