  To describe non-equilibrium transport processes in a quantum device with
infinite baths, we propose to formulate the problems as a reduced-order
problem. Starting with the Liouville-von Neumann equation for the
density-matrix, the reduced-order technique yields a finite system with open
boundary conditions. We show that with appropriate choices of subspaces, the
reduced model can be obtained systematically from the Petrov-Galerkin
projection. The self-energy associated with the bath emerges naturally. The
results from the numerical experiments indicate that the reduced models are
able to capture both the transient and steady states.
