Out-of-equilibrium behavior of quantum vortices : A comparison of point vortex dynamics and Fokker-Planck evolution

Tattersall, R. J. and Baggaley, A. W. and Billam, T. P. (2025) Out-of-equilibrium behavior of quantum vortices : A comparison of point vortex dynamics and Fokker-Planck evolution. Physical review a, 112 (1): 013313. ISSN 1050-2947

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, 0/≲−4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for 0/≳−4, to a value which depends explicitly on the initial conditions for 0/≲−5.