Fermi Liquid in a Torsional Oscillator

We study the transverse acoustic impedance of normal Fermi liquid inside a torsionally oscillating cylindrical container. We use Landau's Fermi liquid theory, and our approach is applicable to both normal 3He and mixtures of 3He in superfluid 4He. The fluid causes dissipation and a change of the resonant frequency of the oscillator. Usually, a liquid medium increases the moment of inertia of the oscillator, but we show that for a suitable choice of container radius and driving frequency, the Fermi liquid can actually decrease the inertia and increase the resonant frequency. Results of numerical calculations for all values of mean free path ℓ are shown and comparison is made to both hydrodynamic theory and simple kinetic theory in the ballistic limit.