  We investigate 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's
function. To benchmark its validity, we compare the solution obtained within
the GKBA with the solution of the Dyson equation (equivalently the full
Kadanoff-Baym equations). In both approaches, we treat the interaction within
the self-consistent second-order Born approximation, whereas the GKBA still
retains the retarded propagator calculated at the Hartree-Fock level. We
consider the case of two leads connected through a central correlated region
where particles can interact and exploit the stationary particle current at the
boundary of the junction as a probe of the spectral features of the system. In
this work, as an example, we take the central region to be a one-dimensional
quantum wire and a two-dimensional carbon nanotube and show that the solution
of the GKBA master equation well captures their spectral features. Our result
demonstrates that, even when the propagator used is at the Hartree-Fock level,
the GBKA solution retains the main spectral features of the self-energy used.
