Theory of Heat Transport of Normal Liquid 3He in Aerogel

The introduction of liquid 3He into silica aerogel provides us a with 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 quasiparticles by the aerogel and inelastic quasiparticle collisions. These results provide quantitative predictions for the transport properties of liquid 3He in aerogel over a wide range of pressure, temperature and aerogel density. In particular, we obtain a scaling function, F(T/T*), for the normalized thermal conductivity, K/K_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.