Self-sustained deformable rotating liquid He cylinders: The pure normal fluid \(^3\)He and superfluid \(^4\)He cases

We have studied self-sustained, deformable, rotating liquid He cylinders of infinite length. In the normal fluid \(^3\)He case, we have employed a classical model where only surface tension and centrifugal forces are taken into account, as well as the Density Functional Theory (DFT) approach in conjunction with a semi-classical Thomas-Fermi approximation for the kinetic energy. In both approaches, if the angular velocity is sufficiently large, it is energetically favorable for the \(^3\)He cylinder to undergo a shape transition, acquiring an elliptic-like cross section which eventually becomes two-lobed. In the \(^4\)He case, we have employed a DFT approach that takes into account its superfluid character, limiting the description to vortex-free configurations where angular momentum is exclusively stored in capillary waves on a deformed cross section cylinder. The calculations allow us to carry out a comparison between the rotational behavior of a normal, rotational fluid (\(^3\)He) and a superfluid, irrotational fluid (\(^4\)He).