Two dimensional Coulomb gas in a non-conservative trap

TL;DR

This paper investigates the steady states of a two-dimensional Coulomb gas under anisotropic trapping and rotational forces, revealing how rotation alters the droplet shape and induces currents, supported by hydrodynamic theory and simulations.

Contribution

It provides a comprehensive analysis of a driven non-equilibrium state in a strongly interacting Coulomb gas with novel shape and current behaviors due to rotation.

Findings

Rotation tilts the elliptical droplet shape.

A nonzero current circulates inside the droplet.

Large rotation leads to a circular droplet form.

Abstract

We study the nonequilibrium steady state of a two dimensional Coulomb gas under the action of an anisotropic harmonic trapping potential along with a non-conservative rotational force. In the case without rotation, the equilibrium (zero temperature) steady state has a uniform density supported over a 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 a fixed angle compared to the non-rotational case. In addition, a nonzero current is generated inside the droplet which run 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 and are confirmed by numerical simulations and provide a full understanding of a novel driven non-equilibrium state in a strongly interacting system.