Self-sustained deformable rotating liquid He cylinders: The pure normal fluid He3 and superfluid He4 cases

Within density functional theory, we have studied self-sustained, deformable, rotating liquid He cylinders subject to planar deformations. In the normal fluid He-3 case, the kinetic energy has been incorporated in a semi-classical Thomas-Fermi approximation. In the He-4 case, our approach takes into account its superfluid character. For this study, we have chosen to limit our investigation to vortex-free configurations where angular momentum is exclusively stored in capillary waves on a deformed cross-section cylinder. Only planar deformations leading to noncircular cross sections have been considered, as they aim to represent the cross section of the very large deformed He drops discussed in the experiments. Axisymmetric Rayleigh instabilities, always present in fluid columns, have been set aside. The calculations allow us to carry out a comparison between the rotational behavior of a normal, rotational fluid (He-3) and a superfluid, irrotational fluid (He-4).