Heat diffusion in the disordered electron gas

We study the thermal conductivity of the disordered two-dimensional electron gas. To this end we analyze the heat density-heat density correlation function concentrating on the scattering processes induced by the Coulomb interaction in the sub-temperature energy range. These scattering processes are at the origin of logarithmic corrections violating the Wiedemann-Franz law. Special care is devoted to the definition of the heat density in the presence of the long-range Coulomb interaction. To clarify the structure of the correlation function, we present details of a perturbative calculation. While the conservation of energy strongly constrains the general form of the heat density-heat density correlation function, the balance of various terms turns out to be rather different from that for the correlation functions of other conserved quantities such as the density-density or spin density-spin density correlation function.