Microscopic Calculation of the Heat Transfer between an Isotropic Superfluid and a Granular Structure

Abstract

We introduce a new model of a sintered metallic powder in which neighbouring grains are either fused together with probability P or weakly coupled with probability (1-P). A new selective renormalization technique is used to compute the density of vibrational states ρ(ω) at wavelengths λ greater than or of order a typical grain size L. For λ≫L, ρ(ω) is Debye-like, whereas for λ>L, a cross over to fracton-like behaviour is observed, consistent with recent experimental results. BCS theory is employed to yield an expression for the heat transfer Q between sinter modes and 3He-B quasi-particles. This expression is combined with ρ(ω) to yield for the first time a fully microscopic evaluation of the temperature dependence of \\dotQ.