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The simulation of quantum transport in a realistic, many-particle system is anontrivial problem with no quantitatively satisfactory solution. Whilereal-time propagation has the potential to overcome the shortcomings ofconventional transport methods, this approach is prone to finite size effectsthat are associated with modeling an open system on a closed spatial domain.Using a master equation framework, we exploit an equivalence between thesuperoperators coupling an open system to external particle reservoirs andnon-Hermitian terms defined at the periphery of a quantum device. By taking themean-field limit, the equation of motion for the single-particle reduceddensity matrix becomes equivalent to real-time time-dependent densityfunctional theory in the presence of imaginary source and sink potentials. Thismethod may be used to converge nonequilibrium steady states for a many-bodyquantum system using a previously reported constraint algorithm.

Complex non-Hermitian Potentials and Real-Time Time-Dependent Density Functional Theory: A Master Equation Approach