Quantum heat transfer in harmonic chains with self consistent   reservoirs: Exact numerical simulations
  We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically-exact results are compared to classical simulations and to the quantum behavior under the linear response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the close-to-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics. 
Malay Bandyopadhyay and Dvira Segal
cond-mat.mes-hall