Harmonic chains and the thermal diode effect

Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly junctions can rectify heat once the (described by white Langevin noise) are placed under temperature gradients, which asymmetric sides, an effect term "temperature-gradient diodes". This nonlinear diode results from additional constraint -- imposed gradient boundaries. We demonstrate rectification behavior based on exact analytical formulation steady state transport in systems coupled to baths, describe quantum and classical transport, both regimes realizing involved boundary conditions. Our study shows systems, such room-temperature hydrocarbon molecules with varying side groups end groups, or a linear lattice trapped ions may going beyond simple