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

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.