Phononic heat transport in the transient regime: An analytic solution
Tuovinen, R., Säkkinen, N., Karlsson, D., Stefanucci, G., & van Leeuwen, R. (2016). Phononic heat transport in the transient regime: An analytic solution. Physical Review B, 93 (21), 214301. doi:10.1103/PhysRevB.93.214301
Published inPhysical Review B
© 2016 American Physical Society. Published in this repository with the kind permission of the publisher.
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. ...