First-principles Wigner formulation of coupled radiative and conductive heat transfer*

At ordinary temperatures, heat transfer in dielectric solids is mainly mediated by atomic vibrations, as accurately described by established quantum transport formulations for heat conduction. At extremely high temperatures, experiments in polar dielectrics show a very strong enhancement in their heat-transfer capability, which departs from predictions obtained using state-of-the-art conduction theories. Such behavior has been speculated to originate from the emergence of additional radiative effects, but no theoretical framework has been able to rationalize it from first principles. 

Here, we employ the Wigner phase-space formulation of quantum mechanics to derive a set of transport equations for coupled conductive and radiative heat transfer. Their first-principles solutions rationalize experiments in materials with various degree of disorder and compositions, as we show with applications to thermal-barrier-coating crystals and oxide glasses. The approach developed sheds lights on the fundamental physics underlying heat transfer in solids, and paves the way for the control and theory-driven optimization of thermal insulators employed e.g. in industrial furnaces, jet engines, and heat shields.