The Heat Capacity of He-3-B in Silica Aerogel

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