Quantum master equation approach to heat transport in dielectrics and semiconductors
- 21 October 2021
- journal article
- research article
- Published by IOP Publishing in Physica Scripta
- Vol. 96 (12), 125022
- https://doi.org/10.1088/1402-4896/ac3201
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.Keywords
This publication has 23 references indexed in Scilit:
- Heat transport in theXXZspin chain: from ballistic to diffusive regimes and dephasing enhancementJournal of Statistical Mechanics: Theory and Experiment, 2013
- Single-Ion Heat Engine at Maximum PowerPhysical Review Letters, 2012
- HEAT CONDUCTION IN DIELECTRIC ATOMIC CHAINS WITH ON-SITE POTENTIALModern Physics Letters B, 2010
- Fourier’s law: Insight from a simple derivationPhysical Review E, 2009
- Fourier’s law of heat conduction: Quantum mechanical master equation analysisPhysical Review E, 2008
- Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equationsPhysical Review B, 2008
- Quantum thermodynamic cycles and quantum heat enginesPhysical Review E, 2007
- Quantum transport using the Ford-Kac-Mazur formalismPhysical Review B, 2003
- Brownian motion of a quantum harmonic oscillatorReports on Mathematical Physics, 1976
- On the generators of quantum dynamical semigroupsCommunications in Mathematical Physics, 1976