Theory of heat transport of normal liquid³He in aerogel

The introduction of liquid ³He into a silica aerogel provides us with a model system in which to study the effects of disorder on the properties of a strongly correlated Fermi liquid. The transport of heat, mass and spin exhibits cross-over behavior from a high temperature regime, where inelastic scattering dominates, to a low temperature regime dominated by elastic scattering off the aerogel. We report exact and approximate solutions to the Boltzmann-Landau transport equation for the thermal conductivity of liquid ³He, including elastic scattering of quasi-particles by the aerogel and inelastic quasi-particle collisions. These results provide quantitative predictions on the transport properties of liquid 3He in aerogels over a wide range of pressures, temperatures and aerogel densities. In particular, we obtain a scaling function, F(T/T*), for the normalized thermal conductivity, κ/κ_el, in terms of a reduced temperature, T/ T*, where T* is a cross-over temperature defined by the elastic and inelastic collision rates. Theoretical results are compared with the available experimental data for the thermal conductivity.