Two-dimensional Coulomb gas in a nonconservative trap

We study the nonequilibrium steady state of a two-dimensional Coulomb gas under the action of an anisotropic harmonic trapping potential along with a nonconservative rotational force. In the case without rotation, the equilibrium (zero temperature) steady state has a uniform density supported over a static elliptical droplet. The addition of a rotational force drives the system into a nonequilibrium steady state where the density is still uniform inside an ellipse, but the ellipse gets tilted by a fixed angle compared to the nonrotational case. In addition, a nonzero current is generated inside the droplet which runs concentrically to the droplet boundary. For large rotational force, the droplet develops a purely circular form. Our results are predicted by a simple hydrodynamic calculation, confirmed by numerical simulations, and provide a full understanding of a driven nonequilibrium state in a strongly interacting system.