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Real-time Green's function simulations of molecular junctions (open quantumsystems) are typically performed by solving the Kadanoff-Baym equations (KBE).The KBE, however, impose a serious limitation on the maximum propagation timedue to the large memory storage needed. In this work we propose a simplifiedGreen's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA)to overcome the KBE limitation on time, significantly speed up thecalculations, and yet stay close to the KBE results. This is achieved through atwofold advance: first we show how to make the GKBA work in open systems andthen construct a suitable quasi-particle propagator that includes correlationeffects in a diagrammatic fashion. We also provide evidence that our GKBAscheme, although already in good agreement with the KBE approach, can befurther improved without increasing the computational cost.

Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast