Self-propelled particle in an external potential: existence of an effective temperature

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 90; no. 1; p. 012111
• Main Author: Szamel, Grzegorz
• Format: Journal Article
• Language: English
• Published: United States 14.07.2014
• Subjects: Models, Theoretical; Motion; Temperature
• ISSN: 1550-2376
• DOI: 10.1103/physreve.90.012111

We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating internal driving force evolving according to the Ornstein-Uhlenbeck process, independently of the state of the particle. Without an external potential, in the long time limit, the self-propelled particle moving in a viscous medium performs diffusive motion, which allows one to identify an effective temperature. We show that in the presence of a linear external potential the stationary state distribution has an exponential form with the sedimentation length determined by the effective temperature of the free self-propelled particle. In the presence of a quadratic external potential the stationary state distribution has a Gaussian form. However, in general, this distribution is not determined by the effective temperature of the free self-propelled particle.