Abstract
Hydrodynamic experiments in quantum liquids at low temperatures are sensitively influenced by the interaction of the elementary excitations with the confining walls of the measuring cell. In the case of transverse oscillations of the walls such that the viscous penetration depth of the liquid is small compared to the container dimensions, the dynamical behavior of the quantum liquid is governed by the transverse surface of shear impedance. We calculate the shear impedance for an isotropic, pair-correlated Fermi liquid from a microscopic quasiparticle Landau-Boltzmann equation using variational methods. A general class of elastic quasiparticle-wall scattering laws is considered in deriving the impedance functional. We give exact results for the variational surface impedance in the low-frequency limit and discuss approximate results in context with special wall-scattering laws such as specular, backward and Andreev scattering. Finally we apply our theory to the experimentally accessible, pair-correlated Fermi liquid3He and particularly investigate the influence of pressure, temperature, frequency, and the parameters specifying the wall-scattering process on the shear impedance.
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Einzel, D., Wölfle, P. & Hirschfeld, P.J. Transverse surface impedance of pair-correlated Fermi liquids. Application to normal and superfluid3He. J Low Temp Phys 80, 31–68 (1990). https://doi.org/10.1007/BF00683113
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DOI: https://doi.org/10.1007/BF00683113