Two-temperature Brownian dynamics of a particle in a confining potential

TL;DR

This paper analyzes the non-equilibrium behavior of a Brownian particle in a confining potential with two different temperatures, revealing a global rotation effect confirmed by simulations and proposed for experimental observation.

Contribution

It provides exact solutions for asymmetric harmonic potentials and introduces a novel non-equilibrium stationary state with a rotation due to temperature and symmetry mismatches.

Findings

Exact solutions for asymmetric harmonic potential in overdamped and underdamped regimes

Identification of a non-zero orthoradial mean current causing rotation

Confirmation of predictions through Brownian dynamics simulations

Abstract

We consider the two dimensional motion of a particle into a confining potential, subjected to Brownian forces, associated with two different temperatures on the orthogonal directions. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes, whereas perturbative approaches are used for more general potentials. The resulting non equilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two symmetry breaking: two different temperatures and a mismatch between the principal axes of the confining asymmetric potential and the temperature axes. We confirm our predictions by performing Brownian dynamics simulation. Finally, we propose to observe this effect on a laser cooled atomic system.