Related papers: Quantum master equation approach to heat transport in dielectrics and semiconductors

Quantum master equation approach to heat transport in dielectrics and semiconductors

URL: http://arxiv.org/abs/2106.13788v3
Date: Wed, 29 Dec 2021 17:44:02 GMT
Title: Quantum master equation approach to heat transport in dielectrics and semiconductors
Authors: Yamen Hamdouni
Abstract summary: We derivationate the heat transport equation for nonmetals using a quantum Markovian master equation in Lindblad form. The effect of the heat reservoir on the lattice is described by a heat source density that depends on the diffusion coefficients of the atoms. The high temperature limit is shown to reproduce the classical heat conduction equation.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We report on the derivation of the heat transport equation for nonmetals using a quantum Markovian master equation in Lindblad form. We first establish the equations of motion describing the time variation of the on-site energy of atoms in a one dimensional periodic chain that is coupled to a heat reservoir. In the continuum limit, the Fourier law of heat conduction naturally emerges, and the heat conductivity is explicitly obtained. It is found that the effect of the heat reservoir on the lattice is described by a heat source density that depends on the diffusion coefficients of the atoms. We show that the Markovian dynamics is equivalent to the long wavelength approximation for phonons, which is typical for the case of elastic solids. The high temperature limit is shown to reproduce the classical heat conduction equation.

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