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

R. J. Tattersall1,*, A. W. Baggaley1,2, and T. P. Billam1

  • 1Joint Quantum Centre Durham-Newcastle, School of Mathematics Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
  • 2Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, United Kingdom

  • *Contact author: r.tattersall2@newcastle.ac.uk
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Phys. Rev. A 112, 013313 – Published 22 July, 2025

DOI: https://doi.org/10.1103/l8yk-kk5c

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, E0/Nv≲−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 2 for E0/Nv≳−4, to a value which depends explicitly on the initial conditions for E0/Nv≲−5.

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Phys. Rev. A 112, 013313– Published 22 July, 2025
  • Received 21 March 2025
  • Accepted 9 June 2025
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