  The generalized Kadanoff-Baym ansatz (GKBA) is an approximation to the
Kadanoff-Baym equations (KBE), that neglects certain memory effects that
contribute to the Green's function at non-equal times. Here we present
arguments and numerical results to demonstrate the practical insignificance of
the quantities neglected when deriving the GKBA at conditions at which KBE and
GKBA are appropriate. We provide a mathematical proof that places a scaling
bound on the neglected terms, further reinforcing that these terms are
typically small in comparison to terms that are kept in the GKBA. We perform
calculations in a range of models, including different system sizes and filling
fractions, as well as experimentally relevant non-equilibrium excitations. We
find that both the GKBA and KBE capture the dynamics of interacting systems
with moderate and even strong interactions well. We explicitly compute terms
neglected in the GKBA approximation and show, in the scenarios tested here,
that they are orders of magnitude smaller than the terms that are accounted
for, i.e., they offer only a small correction when included in the full
Kadanoff-Baym equations.
