Thermodynamic properties of thin films of superfluid ${}^3\mathrm{He}-A$

The pairing correlations in superfluid ${}^3\mathrm{He}$ are strongly modified by quasiparticle scattering off a surface or an interface. We present theoretical results and predictions for the order parameter, the quasiparticle excitation spectrum, and the free energy for thin films of superfluid ${}^3\mathrm{He}.$ Both specular and diffuse scatterings by a substrate are considered, while the free surface is assumed to be a perfectly reflecting specular boundary. The results are based on self-consistent calculations of the order parameter and quasiparticle excitation spectrum at zero pressure. We obtain results for the phase diagram, free energy, entropy, and specific heat of thin films of ${\mathrm{superfluid}}^3\mathrm{He}.$