Time-dependent resonant tunneling transport: Keldysh and Kadanoff-Baym nonequilibrium Greens functions in an analytically soluble problem

Here we address two nonequilibrium Greens functions approaches for a resonant tunneling structure under a sudden switch of a bias. Our aim is to stress that the time-dependent Keldysh formulation of Jauho, Wingreen and Meir, and the partition-free scheme of Stefanucci and Almbladh are formally equivalent in the ubiquitous case of wide-band limit and noninteracting electrons, if leads and dot are in equilibrium before the time-dependent perturbation. We develop explicit closed formulas of the lesser Greens function and time-dependent current, reminding that the different integration limits preclude a face-to-face comparison of two approaches. This study sheds light on both practices, which are of great interest to the mesoscopic transport community.