The Auger process from time dependent density matrix evolution in the GKBA

State-of-the-art experimental techniques allow the stimulation of excited electronic dynamics on an ultra-fast timescale. For example, with XUV radiation it is possible to create highly unstable excited states, which give rise to different relaxation processes of radiative and/or non-radiative nature. As opposed to radiative decay, the nonradiative mechanisms take place on a much faster timescale, i.e. femto- to atto-seconds. A typical decay mechanism enabled by electron correlations is the Auger decay. In this process a secondary electron is expelled from the system to relax to a lower energy state. To describe the Auger mechanism it is key to include electronic correlations otherwise not accounted for in adiabatic time-dependent density functional theory approaches. Within our method we solve the Kadanoff-Baym equations (KBE) in the nonequilibrium Green's function framework by using the generalized Kadanoff-Baym ansatz (GKBA), i.e. recasting the KBE into a computationally more convenient closed equation for the one-particle density matrix. As an illustration we simulate the emission of Auger electrons in real time in one-dimensional atomic systems. This paves the way towards the description of time-dependent Auger decay in realistic systems.