  We consider modifications of the standard non-linear QCD evolution in an
attempt to account for some of the missing ingredients discussed recently, such
as correlations, discreteness in gluon emission and Pomeron loops. The
evolution is numerically performed using the Balitsky-Kovchegov equation on
individual configurations defined by a given initial value of the saturation
scale, for reduced rapidities $y=(\alpha_s N_c/\pi) Y<10$. We consider the
effects of averaging over configurations as a way to implement correlations,
using three types of Gaussian averaging around a mean saturation scale.
Further, we heuristically mimic discreteness in gluon emission by considering a
modified evolution in which the tails of the gluon distributions are cut-off.
The approach to scaling and the behavior of the saturation scale with rapidity
in these modified evolutions are studied and compared with the standard
mean-field results. For the large but finite values of rapidity explored, no
strong quantitative difference in scaling for transverse momenta around the
saturation scale is observed. At larger transverse momenta, the influence of
the modifications in the evolution seems most noticeable in the first steps of
the evolution. No influence on the rapidity behavior of the saturation scale
due to the averaging procedure is found. In the cut-off evolution the rapidity
evolution of the saturation scale is slowed down and strongly depends on the
value of the cut-off. Our results stress the need to go beyond simple
modifications of evolution by developing proper theoretical tools that
implement such recently discussed ingredients.
