  We study transport properties in boundary-driven asymmetric quantum spin
chains given by $\mathit{XXZ}$ and $\mathit{XXX}$ Heisenberg models. Our
approach exploits symmetry transformations in the Lindblad master equation
associated to the dynamics of the systems. We describe the mathematical steps
to build the unitary transformations related to the symmetry properties. For
general target polarizations, we show the occurrence of the one-way street
phenomenon for the energy current, namely, the energy current does not change
in magnitude and direction as we invert the baths at the boundaries. We also
analyze the spin current in some situations, and we prove the uniqueness of the
steady state for all investigated cases. Our results, involving nontrivial
properties of the energy flow, shall interest researchers working on the
control and manipulation of quantum transport.
