  This work reports the study of the spectral properties of an open interacting
system by solving the Generalized Kadanoff-Baym Ansatz (GKBA) master equation
for the single-particle density matrix, namely the time-diagonal lesser Green
function. To benchmark its validity, the solution obtained within the GKBA is
compared with the solution of the Dyson equation at stationarity. In both
approaches, the interaction is treated within the self-consistent second-order
Born approximation, whereas the GKBA still retains the retarded propagator
calculated at the Hartree-Fock and wide-band limit approximation level. The
model chosen is that of two leads connected through a central correlated region
where particles can interact and utilize the stationary particle current at the
boundary of the junction as a probe of the spectral features of the system. The
central region is chosen as the simplest model featuring a degenerate ground
state with a flat band. The main result is that the solution of the GKBA master
equation captures well the spectral feature of such system and specifically the
transition from dispersionless to dispersive behavior of the flat-band as the
interaction is increased. Therefore the GBKA solution retains the main spectral
features of the self-energy used even when the propagator is at the
Hartree-Fock level.
