Einstein-Bose condensation of Onsager vortices

We have studied statistical mechanics of a gas of vortices in two dimensions. We introduce a new observable---a condensate fraction of Onsager vortices---to quantify the emergence of the vortex condensate. The condensation of Onsager vortices is most transparently observed in a single vortex species system and occurs due to a competition between solid body rotation (c.f. vortex lattice) and potential flow (c.f. multiple quantum vortex state). We propose an experiment to observe the condensation transition of the vortices in such a single vortex species system.