Thermal Rectification in Anharmonic Chains under Energy-Conserving Noise

Thermal rectification is the phenomenon in which the heat flux in a given system depends on the direction the flux is applied.
This phenomenon has been widely investigated in recent years due to its great academic and technological relevance. In order to present thermal rectification, at least two main conditions are necessary to such systems: an inherent spacial asymmetry, which breaks the invariance under bath reversal and a temperature dependent thermal conductivity, which induces different phonon spectra when the baths are reversed.
However, in disagreement with the results of experimental works, most results of theoretical models proposed in the literature have a rectification which decreases with increasing system size and thus vanishes in the thermodynamic limit. So, since these ingredients may not suffice to maintain a finite thermal rectification, we introduce a new ingredient, namely energy-conserving noise that randomly flips the sign of the velocity of the system's particles with a certain rate $\lambda$. With this new ingredient, we show that a finite and non-zero thermal rectification in the thermodynamic limit can be obtained. Our analysis is done numerically, with the simulation of a harmonic chain subject to a quartic local potential (pinning) and coupled at its ends to thermal reservoirs by Langevin equations.