Waiting time distribution of quantum electronic transport in the transient regime

Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady-state transport (either dc or ac). The existing theory cannot deal with WTD in the transient regime. In this regard, we develop a theoretical formalism based on Keldysh nonequilibrium Green's-function formalism to study WTD. This theory is suitable for dc, ac, and transient transport and can be used for first-principles calculation on realistic systems. We apply this theory to a quantum dot system with an upward bias pulse and calculate cumulants of transferred charge as well as WTD in the transient regime. The oscillatory behavior of WTD is found in the transient regime. We give a general relation between WTD and experimental measured quantity and demonstrate its feasibility for a quantum dot system in the transient regime.