Effect of container walls on vibrating wire in 3He-4He mixtures in the ballistic limit

Abstract

We study linearized kinetic equations describing mixtures of 3He and 4He at such low temperatures, that all of 4He is superfluid. The 3He part is described by Landau's Fermi liquid theory, in the form derived by Khalatnikov in the case of mixtures. Here we apply the theory to the case of vibrating wire. The linearized Landau-Boltzmann kinetic equation with relaxation time approximation needs to be solved numerically at finite temperatures. In the ballistic limit, the collision term in the equation vanishes, enabling an analytic approach. There are many features affecting the system, including the coupling of 3He to the superfluid 4He, the effect of Fermi liquid interactions, and the dependence on the frequency ω of the vibrating wire. Also, the type of scattering of the quasiparticles from the surface of the wire can be either specular or diffusive. In this paper, we consider the effects of chamber walls near the wire. It has been speculated that the nearness of the container walls has affected the experimental results of Martikainen et al.. We find that the presence of container walls near a slowly moving wire increases the dissipation experienced by the wire.