Energy diffusion in disordered electronic systems near the Anderson transition

The problem of heat diffusion for a noninteracting electron gas scattered by random impurities is formulated in terms of a frequency- and wave-vector-dependent grand canonical energy-energy (heat-heat) correlation function χKK(q;{ω}). Consistently with a Ward identity associated with the continuity equation for heat diffusion, we show that the heat-heat correlation function has the same critical diffusive behavior of the density-density correlation function. This result enables us, in particular, to predict that the electrical conductivity and the thermal conductivity (times the inverse temperature) of metals scale to zero in the same way near the Anderson transition.