Abstract
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. Specifically we consider a dissipative boundary driven ladder in the presence of a gauge field that can be implemented with ion microtrap arrays. We show that, depending on the geometry, the currents imposed by the baths can be strongly affected by the gauge field, resulting in nonequilibrium phase transitions. In different phases both the magnitude of the current and its spatial distribution are significantly different. These findings allow for strategies to manipulate and control transport properties in quantum systems.