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To describe non-equilibrium transport processes in a quantum device withinfinite baths, we propose to formulate the problems as a reduced-orderproblem. Starting with the Liouville-von Neumann equation for thedensity-matrix, the reduced-order technique yields a finite system with openboundary conditions. We show that with appropriate choices of subspaces, thereduced model can be obtained systematically from the Petrov-Galerkinprojection. The self-energy associated with the bath emerges naturally. Theresults from the numerical experiments indicate that the reduced models areable to capture both the transient and steady states.

A reduced-order modeling approach for electron transport in molecular junctions