  This work is devoted to the investigation of nontrivial transport properties
in many-body quantum systems. Precisely, we study transport in the steady state
of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic
baths with fixed, different magnetization. We take graded versions of the
model, i.e., asymmetric chains in which some structure gradually changes in
space. We investigate how we can manipulate and control the energy and spin
currents of such chains by tuning external and/or inner parameters. In
particular, we describe the occurrence of energy current rectification and its
reversal due to the application of external magnetic fields. We show that,
after carefully chosen the inner parameters of the system, by turning on an
external magnetic field we can find spin and energy currents propagating in
different directions. More interestingly, we may find cases in which
rectifications of the energy and of the spin currents occur in opposite
directions, i.e., if the energy current is larger when flowing from left to
right side, then the spin current is larger if it flows from the right to left
side. We still describe situations with inversion of the energy current
direction as we increase the system asymmetry. We stress that our work aims the
development of theoretical knowledge as well as the stimulation of future
experimental applications.
