Heat transport in ordered and disordered solids within Wigner’s phase-space formulation*

We explore the atomistic mechanisms of thermal transport in solids using Wigner’s [Phys. Rev. 40 (1932)] phase-space formulation of quantum mechanics, showing how this formalism allows to derive a heat-transport equation that describes on an equal footing heat conduction in crystals, glasses, and anything in between [Simoncelli, Marzari, and Mauri, Nat. Phys., 15 (2019)]. We use this framework to shed light on formal aspects of the theory of thermal transport in solids, including the description of local equilibrium (i.e., the state associated to a space-dependent temperature) and the differences between Wigner’s [Nat. Phys., 15 (2019)] and Hardy’s [Phys. Rev. 132 (1963)] expressions for the heat flux.
Finally, we use first-principles calculations to show the capability of Wigner’s formulation to predict correctly and in agreement with experiments the opposite trends of thermal conductivity in ordered and disordered solids.