Motivated by the demand of efficient quantum devices to engineer the energytransport, we analyze some inhomogeneous quantum spin systems, including theXXZ chains, with magnetization baths at the ends. Aimed at finding generalproperties, we study the effects of suitable transformations on theboundary-driven Lindblad master equation associated to the dynamics of thesystems. For asymmetric models with target polarization at the edges or twistedXY boundary gradients, we show properties of the steady state which establishfeatures of the energy current, irrespective of the system size and of theregime of transport. We show the ubiquitous occurrence of energy rectificationand, more interestingly, of an unusual phenomenon: in the absence of externalmagnetic field, there is an one-way street for the energy current, i.e., thedirection of the energy current does not change as we invert the magnetizationbaths at the boundaries. Given the extensiveness of the procedures, whichessentially involve properties of the Lindblad master equation, our resultscertainly follow for other interactions and other boundary conditions.Moreover, our results indicate graded spin chains as genuine quantumrectifiers.
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