2021/06/25 by Yamen Hamdouni
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed matter physics #Diffusion equation #Heat current #Heat equation #Heat transfer #Limit (mathematics) #Lindblad equation #Long wavelength limit #Master equation #Mathematical analysis #Mathematics #Phonon #Physics #Quantum #Quantum master equation #Quantum mechanics #Semiconductor Quantum Structures and Devices #Thermal Radiation and Cooling Technologies #Thermal conduction #Thermal conductivity #Thermal properties of materials #Thermal reservoir #cond-mat.other #cond-mat.stat-mech #quant-ph
paper · pdf · open access · doi:10.1088/1402-4896/ac3201
published in Physica Scripta 96(12), 125022 (IOP Publishing)
openalex publication_date 2021/10/21 · arxiv created 2021/12/29 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.