Nonequilibrium perturbation theory of the spinless Falicov-Kimball model: Second-order truncated expansion inU

We perform a perturbative analysis for the nonequilibrium Green's functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction-electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green's functions from a transient-response formalism (in infinite dimensions) on the Kadanoff-Baym-Keldysh contour. We find that a strictly truncated perturbation theory in the two-time formalism cannot reach the long-time limit of the steady state; instead, it illustrates pathological behavior for times larger than approximately $2∕U$.