  Experimental stirring of a toroidally trapped Bose-Einstein condensate at
high temperature generates a disordered array of quantum vortices that decays
via thermal dissipation to form a macroscopic persistent current [T. W. Neely
em et al. arXiv:1204.1102 (2012)]. We perform 3D numerical simulations of the
experimental sequence within the Stochastic Projected Gross-Pitaevskii equation
using ab initio determined reservoir parameters. We find that both damping and
noise are essential for describing the dynamics of the high-temperature Bose
field. The theory gives a quantitative account of the formation of a persistent
current, with no fitted parameters.
