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We have developed a method based on the embedded Kadanoff-Baym equations tostudy the time evolution of open and inhomogeneous systems. The equation ofmotion for the Green's function on the Keldysh contour is solved usingdifferent conserving many-body approximations for the self-energy. Ourformulation incorporates basic conservation laws, such as particleconservation, and includes both initial correlations and initial embeddingeffects, without restrictions on the time-dependence of the external drivingfield. We present results for the time-dependent density, current and dipolemoment for a correlated tight binding chain connected to one-dimensionalnon-interacting leads exposed to DC and AC biases of various forms. We findthat the self-consistent 2B and GW approximations are in extremely goodagreement with each other at all times, for the long-range interactions that weconsider. In the DC case we show that the oscillations in the transients can beunderstood from interchain and lead-chain transitions in the system and findthat the dominant frequency corresponds to the HOMO-LUMO transition of thecentral wire. For AC biases with odd inversion symmetry odd harmonics to highharmonic order in the driving frequency are observed in the dipole moment,whereas for asymmetric applied bias also even harmonics have considerableintensity. In both cases we find that the HOMO-LUMO transition strongly mixeswith the harmonics leading to harmonic peaks with enhanced intensity at theHOMO-LUMO transition energy.

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields