From Green-Kubo to the full Boltzmann kinetic approach to heat transport in crystals and glasses

We show that vertex corrections to the quasiharmonic Green-Kubo theory of heat transport in insulators naturally lead to a generalization of the expression for the conductivity that could be derived from the linearized Boltzmann equation, when the effects of the full scattering matrix are accounted for. Our results, which are obtained from the Mori-Zwanzig memory-function formalism, provide a fully ab initio derivation of the linearized Boltzmann transport equation and establish a connection between two recently proposed unified approaches to heat transport in insulating crystals and glasses.