Topological aspects of persistent flows in 3He-A in a toroidal container
The isotope 3He can exist in different superfluid states depending on the external conditions. In this paper the authors consider 3He in its A phase and use topological arguments to gain some insight into persistent currents which they also refer to as ``quantised flows''. The authors take as their starting point the phenomenological picture of \textit{N. D. Mermin} [J. Math. Phys. 19, 1457-1467 (1978; Zbl 0398.55015)], who has argued that the problem of persistent currents in a toroidal container is equivalent to the problem of classifying all continuous maps from the solid torus to the order parameter space of 3He-A subject to the restrictions brought about in this space by the boundary conditions. However since Mermin's arguments were incomplete it is the purpose of the present paper to give a simple but complete topological explanation of the problem. They conclude that although quantised flows on the surface can extend to flows inside the container in a continuous way the flow need no longer be quantised inside the torus. However energy considerations are ignored in this work and as is pointed out by the authors the topological deformations necessary to bring about this situation may not be energetically favourable.
scientific article; zbMATH DE number 4045421