Fermi liquid theory applied to vibrating wire measurements in 3He-4He mixtures

Abstract: We use Fermi liquid theory to study the mechanical impedance of 3He-4He mixtures at low temperatures. The theory is applied to the case of vibrating wires, immersed in the liquid. We present numerical results based on a direct solution of Landau-Boltzmann equation for the 3He quasiparticle distribution for the full scale of the quasiparticle mean-free-path. The two-fluid nature of mixtures is taken into account in the theory, and the effect of Fermi liquid interactions and boundary conditions are studied in detail. The results are in fair quantitative agreement with experimental data. In particular, we can reproduce the anomalous decrease in inertia, observed in vibrating wire experiments reaching the ballistic limit. The essential effect of the experimental container and second-sound resonances is demonstrated.