Second-Sound Velocity, Scaling, and Universality in He II under Pressure near the Superfluid Transition

Abstract

The velocity of second sound in He II was measured for $\ensuremath{\epsilon}\ensuremath{\equiv}1\ensuremath{-}\frac{T}{{T}_{\ensuremath{\lambda}}}>~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ between saturated vapor pressure (SVP) and the melting curve. For $P>\mathrm{SVP}$, the corresponding superfluid fraction $\frac{{\ensuremath{\rho}}_{s}}{{\ensuremath{\rho}}^{\ensuremath{'}}}$ cannot be described by a simple power law in $\ensuremath{\epsilon}$. When reasonable general assumptions are made about higher-order singular contributions, the asymptotic behavior of $\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$ may be deduced and agrees well with scaling and universality.