Quantization of Macroscopic Motions and Hydrodynamics of Rotating Helium II

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 vₒ=0. 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 vₒ= (2m) ₕ (r-rₕ), that is, Landau's requirement is valid everywhere excluding singular lines where the curl is equal to infinity (rₕ is a two-dimensional radius vector of a vortex line in an arbitrary plane perpendicular to the axis of rotation). In the review the experiments are described in which both an averaged picture of the joint rotation of the superfluid and the normal components is displayed and the studies in which the existence of vortex peculiarities is manifested in a clear manner. The measurements of the meniscus of rotating helium ii and its angular momentum belong to the first group of these experiments ("integral" ones). Propagation of second sound, oscillations of solid bodies immersed into helium ii, passage of negative ions, and different relaxation processes (acceleration and deceleration of the vessel, changes of temperature, etc. ) from the second group ("local" experiments). The experiments in which the superfluid performs potential rotation, which can be persistent in the vessel at rest are also described. Vortex lines are absent there and the circulation of velocity can reach the value equal to a lot of elementary circulations. Special attention is devoted to the problem of the nature of the phase transition helium i-helium ii (and back) in the state of rotation. The properties of rotating helium ii illustrate brightly the main peculiarity of a quantum liquid, i. e. , its complete inability to perform nonpotential motions. They show that Landau's requirement curl vₒ=0 remains valid even when the thermodynamical condition of the free-energy (E-L₀) minimization gives preferrence to the velocity distribution of the type v=₀r.