  Motivated by the demand of efficient quantum devices to engineer the energy
transport, we analyze some inhomogeneous quantum spin systems, including the
XXZ chains, with magnetization baths at the ends. Aimed at finding general
properties, we study the effects of suitable transformations on the
boundary-driven Lindblad master equation associated to the dynamics of the
systems. For asymmetric models with target polarization at the edges or twisted
XY boundary gradients, we show properties of the steady state which establish
features of the energy current, irrespective of the system size and of the
regime of transport. We show the ubiquitous occurrence of energy rectification
and, more interestingly, of an unusual phenomenon: in the absence of external
magnetic field, there is an one-way street for the energy current, i.e., the
direction of the energy current does not change as we invert the magnetization
baths at the boundaries. Given the extensiveness of the procedures, which
essentially involve properties of the Lindblad master equation, our results
certainly follow for other interactions and other boundary conditions.
Moreover, our results indicate graded spin chains as genuine quantum
rectifiers.
