Effective classical harmonic crystal with thermal rectification

We prove the existence of a thermal rectification mechanism in a harmonic model with a temperature-dependent effective potential. In contrast to much earlier work where it was shown for this model that rectification occurs in short chains of up to six sites, we analytically prove that this phenomenon occurs in a material with graded mass distribution for any size of the chain and is independent of the regime of heat transport. We find that thermal rectification is observed in a system with other asymmetric parameters, which can be related to structure parameters of the system or to features that depend on the temperatures of the internal sites of the chain and change when the heat baths at ends of the chain exchange places. The description of thermal rectification in these simplified models with a minimal set of ingredients shows that the phenomenon is ubiquitous and can help to theoretically investigate and practically create an efficient thermal diode.