Stochastic theory of the nucleation of quantized vortices in superfluid helium

The problem of the appearance of quantized vortex lines and rings in superflow, and the modification of that flow by the vortices, is examined in the light of a suggestion by Iordanskii, namely that thermal fluctuations may play a vital role in the nucleation process. The view is taken that there exists a distribution of quantized vortex rings in liquid helium and that the smallest of these is a roton. The evolution of these rings in a counterflow is examined by means of a Langevin equation. A Fokker-Planck equation is developed, and a number of examples are presented which illustrate the features of such processes. These include nucleation of vortices in an unbounded fluid, nucleation in a finite channel, the thermally activated vortex mill, nucleation of vortices by ions and phonon-roton relaxation times.