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The Heat Capacity of \(^3\)He-B in Silica Aerogel

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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 \({\mathbf s} =k_{\text {B}}T_c/E_f\). 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 \(p=11-29\,\text{ bar }\). The analysis supports a conclusion that superfluid \(^3\)He-B infused into high-porosity silica aerogels is a gapless superfluid at all pressures.

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Acknowledgements

This research was supported by National Science Foundation Grant DMR-1508730. I thank Bill Halperin and Hyoungsoon Choi for discussions on their experiments and for providing me with their published heat capacity data.

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  1. Department of Physics and Astronomy, Hearne Institute of Theoretical Physics, Louisiana State University, Baton Rouge, LA, 70803, USA

    J. A. Sauls

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Sauls, J.A. The Heat Capacity of \(^3\)He-B in Silica Aerogel. J Low Temp Phys 213, 42–50 (2023). https://doi.org/10.1007/s10909-023-02996-w

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