A direct solution to the phonon Boltzmann equation

TL;DR

This paper introduces a novel integral equation approach for solving the frequency-dependent phonon Boltzmann equation, enabling calculation of static and dynamic thermal conductivities in materials like C, Si, and Mg2Si.

Contribution

It presents a new spectral method that diagonalizes the collision kernel and symmetry operators to solve the phonon Boltzmann equation at finite frequencies.

Findings

Successfully computed static and dynamical thermal conductivities for C, Si, and Mg2Si.

Demonstrated the method's applicability to different materials.

Provided insights into phonon transport at finite frequencies.

Abstract

The frequency dependent phonon Boltzmann equation is transformed to an integral equation over the irreducible part of the Brillouin zone. Simultaneous diagonalization of the collision kernel of that equation and a symmetry crystal class operator allow to obtain a spectral representation of the lattice thermal conductivity valid at finite frequency. The method is applied to C, Si and Mg$_2$Si to obtain the static and dynamical thermal conductivities.