Magnonic thermal transport using the quantum Boltzmann equation

TL;DR

This paper derives a quantum Boltzmann equation for Bose systems, specifically magnons, revealing how quantum effects modify thermal conductivity beyond classical approximations.

Contribution

It introduces a new formula for thermal transport in Bose systems based on the quantum Boltzmann equation, including quantum corrections to conventional models.

Findings

Quantum Boltzmann equation derived for Bose systems.

Thermal conductivity exhibits quantum corrections beyond classical Boltzmann.

Quasiparticle approximation enhances thermal conductivity through self-energy corrections.

Abstract

We present a formula for thermal transport in the bulk of Bose systems based on the quantum Boltzmann equation (QBE). First, starting from the quantum kinetic equation and using the Born approximation for impurity scattering, we derive the QBE of Bose systems and provide a formula for thermal transport subjected to a temperature gradient. Next, we apply the formula to magnons. Assuming a relaxation time approximation and focusing on the linear response regime, we show that the longitudinal thermal conductivity of the QBE exhibits the different behavior from the conventional. The thermal conductivity of the QBE reduces to the Drude-type in the limit of the quasiparticle approximation, while not in the absence of the approximation. Finally, applying the quasiparticle approximation to the QBE, we find that the correction to the conventional Boltzmann equation is integrated as the self-energy into the spectral function of the QBE, and this enhances the thermal conductivity. Thus we shed light on the thermal transport property of the QBE beyond the conventional.