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We derive frequency moment sum rules for the retarded electronic Green'sfunction and self-energy of the Holstein model for both equilibrium andnonequilibrium cases. We also derive sum rules for the phonon propagator inequilibrium and nonequilibrium. These sum rules allow one to benchmarknonequilibrium calculations and help with interpreting the behavior ofelectrons driven out of equilibrium by an applied electric field. We exactlyevaluate the sum rules when the system is in the atomic limit. We also discussthe application of these sum rules to pump/probe experiments like time-resolvedangle-resolved photoemission spectroscopy.

Nonequilibrium sum rules for the Holstein model