The Heat Capacity of ${}^3$He-B in Silica Aerogel

Abstract

The thermodynamic potential for superfluid ${}^3$He-B embedded in a homogeneously distributed random potential is calculated from a quasiclassical reduction of the Luttinger-Ward functional to leading order in $k_{\mbox{$\tiny B$}} T_c/E_f$. The resulting functional provides an extension of the Ginzburg-Landau free energy functional to all temperatures $0<T\le T_c$. Theoretical predictions based on this functional for the heat capacity of superfluid ${}^3$He-B embedded in homogeneous, isotropic silica aerogel are in good agreement with experimental reports for superfluid ${}^3$He-B infused into 98.2% porous silica aerogel over the pressure range $p=11 - 29\,\mbox{bar}$. The analysis supports a conclusion that superfluid ${}^3$He-B infused into high-porosity silica aerogels is a gapless superfluid at all pressures.

arXiv comment8 pages, 6 figures

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