The temperature dependent thermal potential in Quantum Boltzmann equation

TL;DR

This paper investigates the microscopic origins of thermal potentials in quantum systems by deriving them from the quantum Boltzmann equation, considering temperature effects, scattering processes, and quantum corrections, with numerical validation.

Contribution

It provides a microscopic derivation of thermal scalar and vector potentials from the quantum Boltzmann equation, incorporating temperature dependence and quantum corrections.

Findings

Derived thermal potentials from damping force related to electron scattering.

Numerical results show temperature and gradient effects on thermal current.

Quantum corrections influence damping force and anomalous velocity.

Abstract

To explore the thermal transport procedure driven by temperature gradient in terms of linear response theory, Luttinger et al. proposed the thermal scalar and vector potential[1,2] . In this manuscript, we try to address the microscopic origin of these phenomenological thermal potentials. Based on the temperature dependent damping force derived from quantum Boltzmann equation (QBE), we express the thermal scalar and vector potential by the distribution function in damping force, which originates from the scattering of conduction electrons. We illustrate this by the scattering of electron-phonon interaction in some systems. The temperature and temperature gradient in the local equilibrium distribution function will have effect on the thermal scalar and vector potentials, which is compatible with the previous works[1,2] . The influence from quantum correction terms in QBE are also considered, which contribute not only to the damping force, but also to the anomalous velocity in the drift term. An approximated solution for the QBE is given, the numerical results for the damping force, thermal current density as well as other physical observable are shown in figures.