Viscosity of liquid He-4 and quantum of circulation: Why and how are they related?

Abstract

The relationship between the apparently unrelated physical quantities -- kinematic viscosity of liquid He-4, $\nu$, and quantum of circulation, $\kappa=2\pi \hbar/m_4$, where $\hbar$ is the Planck constant and $m_4$ denotes the mass of the $^4$He atom -- is examined in the vicinity of the superfluid transition occurring due to Bose-Einstein condensation. A model is developed, leading to the surprisingly simple relation $\nu \approx \kappa/6$. We critically examine the available experimental data for $^4$He relevant to this simple relation and predict the kinematic viscosity for the stretched liquid $^4$He along the $\lambda$-line at negative pressures.