Non-equilibrium Green's function approach to inhomogeneous quantum   many-body systems using the Generalized Kadanoff Baym Ansatz
  In non-equilibrium Green's function calculations the use of the Generalized Kadanoff-Baym Ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green's function from its time-diagonal value. With this a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present results for a 2-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for the correct description of the equilibrium and dynamic properties. 
S. Hermanns, K. Balzer, and M. Bonitz
cond-mat.str-el