  We consider the SU(2) Glasma with gaussian fluctuations and study its
evolution by means of classical Yang-Mills equations solved numerically on a
lattice. Neglecting in this first study the longitudinal expansion we follow
the evolution of the pressures of the system and compute the effect of the
fluctuations in the early stage up to $t\approx 2$ fm/c, that is the time range
in which the Glasma is relevant for high energy collisions. We measure the
ratio of the longitudinal over the transverse pressure, $P_L/P_T$, and we find
that unless the fluctuations carry a substantial amount of the energy density
at the initial time, they do not change significantly the evolution of
$P_L/P_T$ in the early stage, and that the system remains quite anisotropic. We
also measure the longitudinal fields correlators both in the transverse plane
and along the longitudinal direction: while at initial time fields appear to be
anticorrelated in the transverse plane, this anticorrelation disappears in the
very early stage and the correlation length in the transverse plane increases;
on the other hand, we find that the longitudinal correlator decreases for a
small longitudinal separation while being approximately constant for larger
separation, which we interpret as a partial loss of longitudinal correlation
induced by the dynamics.
