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

TL;DR

This paper derives a comprehensive theoretical framework connecting Green-Kubo and Boltzmann approaches to heat transport in insulators, incorporating vertex corrections and the full scattering matrix from first principles.

Contribution

It provides an ab initio derivation of the linearized Boltzmann transport equation including vertex corrections, unifying approaches for crystals and glasses.

Findings

Vertex corrections lead to a generalized conductivity expression.

The Mori-Zwanzig formalism bridges Green-Kubo and Boltzmann theories.

Unified description applies to both crystals and glasses.

Abstract

We show that vertex corrections to the quasi-harmonic Green-Kubo theory of heat transport in insulators naturally lead to a generalisation 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.