Spin-up and nucleation of vortices in superfluid He-4

It is shown that the Ginzburg-Landau model corrected for the normal component describes adequately the spin-up problem for the superfluid liquid helium. An analysis of the Eckhaus instability in an inhomogeneous rotationally invariant system is presented. It has been found that the number of vortices which can be nucleated at the threshold of instability scales with the radius of the container as R(3/4). Th, effect of excitation of the vortex loops by thermal fluctuations is considered, and the barrier and the nucleation rate are evaluated.