Thermal rectification in quantum graded mass systems

We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in this effective, simple model (representing graded mass materials, systems that may be constructed in practice) indicates that rectification in graded mass quantum systems may be an ubiquitous phenomenon. Moreover, as the classical version of this model does not present rectification, our results show that, here, rectification is a direct result of the quantum statistics.