One-dimensional Excitations in Superfluid ⁴He and ³He-⁴He Mixture Films Adsorbed in Porous Materials

A normal-fluid component varying as T$^{2}$ is observed at very low temperatures in superfluid $^4$He and $^3$He-$^4$He mixture films adsorbed in alumina powder. The normal fluid appears to arise from thermally excited third sound that has one-dimensional propagation characteristics. A Landau model of third sound excitations in an infinite cylindrical pore by Saam and Cole provides good agreement with the experimental measurements over a wide range of $^4$He and $^3$He coverages. However, it is unclear why the powder substrate can be modeled as having cylindrical pores.