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Nonequilibrium Green's functions provide a powerful tool for computing thedynamical response and particle exchange statistics of coupled quantum systems.We formulate the theory in terms of the density matrix in Liouville space andintroduce superoperator algebra that greatly simplifies the derivation and thephysical interpretation of all quantities. Expressions for various observablesare derived directly in real time in terms of superoperator nonequilibriumGreen's functions (SNGF), rather than the artificial time-loop required inSchwinger's Hilbert-space formulation. Applications for computing interactionenergies, charge densities, average currents, current induced fluorescence,electroluminescence and current fluctuation (electron counting) statistics arediscussed.

Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions