  Quantum systems in contact with an environment display a rich physics
emerging from the interplay between dissipative and Hamiltonian terms. Here we
focus on the role of the geometry of the coupling between the system and the
baths. In the specific we consider a dissipative boundary driven ladder in
presence of a gauge field which can be implemented with ion microtraps arrays.
We show that, depending on the geometry, the currents imposed by the baths can
be strongly affected by the gauge field resulting in non-equilibrium phase
transitions. In different phases both the magnitude of the current and its
spatial distribution are significantly different. These findings allow for
novel strategies to manipulate and control transport properties in quantum
systems.
