Transition from Hydrodynamic to Ballistic Quasiparticle Behavior in a Fermi Gas: The Response of a Vibrating-Wire Resonator in aHe3-He4Solution from 0.3 to 10 mK

Measurements of the frequency shift, $\Delta f_1$, and the damping, $\Delta f_2$, of a vibrating wire in a saturated ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solution are reported. A transition is observed in the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle Fermi gas from a hydrodynamic regime at 10 mK to a collisionless-excitation gas regime at the lowest temperatures, < 0.3 mK, where the mean free path becomes extremely long. The comparison between $\Delta f_1$ and $\Delta f_2$ supports the slip theory of Højgaard Jensen et al. with the recent modification proposed by Carless, Hall, and Hook.