Out of Equilibrium Behaviour of Quantum Vortices: A Comparison of Point Vortex Dynamics and Fokker-Planck Evolution

Abstract

An out of equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well-approximated by Fokker-Planck evolution only for very low initial energies per vortex, approximately less than -4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent, $z$, in the dissipative point vortex model, undergoes a crossover, from a roughly constant value close to two for energy per vortex approximately greater than -4 to one which depends explicitly on the initial conditions for energy per vortex approximately less than -5.