6533b82bfe1ef96bd128d7b0
RESEARCH PRODUCT
Phononic heat transport in the transient regime: An analytic solution
Gianluca StefanucciGianluca StefanucciRobert Van LeeuwenNiko SäkkinenDaniel KarlssonRiku Tuovinensubject
PhononEnergy dispersionphononsFOS: Physical sciencesNon-equilibrium thermodynamics02 engineering and technology01 natural sciencesSettore FIS/03 - Fisica della MateriaQuantum transportMesoscale and Nanoscale Physics (cond-mat.mes-hall)0103 physical sciencesElectronicOptical and Magnetic Materials010306 general physicsquantum transportfononitElectronic Optical and Magnetic Materials; Condensed Matter PhysicsPhysicsCondensed Matter - Mesoscale and Nanoscale PhysicsAnalytical expressionsta114Equations of motionCondensed Matter Physics021001 nanoscience & nanotechnologyClassical mechanicsReduced density matrix0210 nano-technologyAnalytic solutionheat transportdescription
We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Green's function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approximation against full numerical solutions of the bosonic Kadanoff--Baym equations for the Green's function. We find good agreement between the analytic and numerical solutions for weak contacts and baths with a wide energy dispersion. We further analyze relaxation times from low to high temperature gradients.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |