A statistical mechanical approach of self-organization of a quantised vortex gas in a two-dimensional superfluid

In this work the relaxation of a two-dimensional Bose-gas from a non-equilibrium initial condition consisting of vortices is studied. To focus on the role of the vortex excitations on the time evolution of the system, a point vortex model is used. The relaxation of the vortex gas is seen to lead to clustering of like-signed vortices that can be explained in terms of negative temperature states. The nature of the Coulomb interactions between vortices, precludes a well-defined thermodynamic limit. The large scale flow structures, therefore strongly depend on the shape of the geometry. These structures can be explained in terms of a maximum entropy principle for the vortex gas that leads to the Boltzmann-Poisson equation. For a square region the maximum entropy configuration corresponds to a monopole. This configuration results in the spontaneous acquisition of angular momentum by the ow. However, by stretching the square domain into a rectangle, the configuration which maximises the entropy switched to a dipole where like-signed vortices tend to equally occupy the two halves of the domain. In this case, the mean flow has zero angular momentum. A direct qualitative and quantitative comparison between the predictions of the mean-field theory and dynamical simulations of a point vortex model are presented. In particular, we show that vortex-antivortex annihilation results in evaporative heating of the vortex gas and the subsequent migration of the system into the negative temperature regime. Moreover, the study is extended to the dynamics of quantised vortices in the same confined geometries in a two-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Despite the coexistence of phonons with vortex excitations that interact together, the above predictions continue to apply in this more realistic model of a two-dimensional superfl uid