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arXiv · 1604.02298

Phononic heat transport in the transient regime: An analytic solution

Riku Tuovinen·Niko Säkkinen·Daniel Karlsson·Gianluca Stefanucci·Robert van Leeuwen
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Abstract

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.

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Riku Tuovinen, Niko Säkkinen, Daniel Karlsson, Gianluca Stefanucci, Robert van Leeuwen. 2016-05-18. Phononic heat transport in the transient regime: An analytic solution. https://doi.org/10.1103/physrevb.93.214301

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