Exact asymptotics of the current in boundary-driven dissipative quantum chains in large external fields

A boundary-driven quantum master equation for a general inhomogeneous (nonintegrable) anisotropic Heisenberg spin-1/2 chain, or an equivalent nearest neighbor interacting spinless fermion chain, is considered in the presence of a strong external field f. We present an exact closed form expression for large f asymptotics of the current in the presence of a pure incoherent source and sink dissipation at the boundaries. In application, we demonstrate an arbitrary large current rectification in the presence of the interaction.