Quantization of Macroscopic Motions and Hydrodynamics of Rotating Helium II

Abstract

This paper is a review of experimental data and theoretical studies devoted to the rotating helium ii problem. The problem arose when helium ii appeared to be rotating as a whole in a uniformly rotated container, while dragging of its superfluid component into rotation of a cylindrical vessel seemed impossible due to the absence of viscosity and Landau's requirement curl ${\mathrm{v}}_s=0\mathrm{}$. Later it was found that imitation of a solid body rotation by helium ii is realized by means of Onsager-Feynman's vortex lines which possess quantized circulation. In a uniformly rotating vessel they are distributed approximately uniformly along its cross section, aligned parallel to the axis of rotation, and cause a complicated velocity distribution at which curl ${\mathrm{v}}_s=\left(\frac{2\pi \hslash }{m}\right){\Sigma }_v\delta (\mathrm{r}-{\mathrm{r}}_v)$, that is, Landau's requirement is valid everywhere excluding singular lines where the curl is equal to infinity (${\mathrm{r}}_v$ is a two-dimensional radius vector of a vortex line in an arbitrary plane perpendicular to the axis of rotation).