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arXiv · 1404.0765

A self-propelled particle in an external potential: is there an effective temperature?

Grzegorz Szamel
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Abstract

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 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.

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Grzegorz Szamel. 2014-04-03. A self-propelled particle in an external potential: is there an effective temperature?. https://doi.org/10.1103/physreve.90.012111

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