  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 harmonic junctions can rectify
heat once the reservoirs (described by white Langevin noise) are placed under
temperature gradients, which are asymmetric at the two sides, an effect that we
term "temperature-gradient harmonic oscillator diodes". This nonlinear diode
effect results from the additional constraint -- the imposed thermal gradient
at the boundaries. We demonstrate the rectification behavior based on the exact
analytical formulation of steady state heat transport in harmonic systems
coupled to Langevin baths, which can describe quantum and classical transport,
both regimes realizing the diode effect under the involved boundary conditions.
Our study shows that asymmetric harmonic systems, such as room-temperature
hydrocarbon molecules with varying side groups and end groups, or a linear
lattice of trapped ions may rectify heat by going beyond simple boundary
conditions.
