Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields

We derive exact operator average expressions for the first two spectral moments of nonequilibrium Green's functions for the Falicov-Kimball model and the Hubbard model in the presence of a spatially uniform, time-dependent electric field. The moments are similar to the well-known moments in equilibrium, but we extend those results to systems in arbitrary time-dependent electric fields. Moment sum rules can be employed to estimate the accuracy of numerical calculations; we compare our theoretical results to numerical calculations for the nonequilibrium dynamical mean-field theory solution of the Falicov-Kimball model at half-filling.