  We study systematically the topological charge density and the chiral density
correlations in the early stage of high energy nuclear collisions: the intial
condition is given by the McLerran-Venugopalan model and the evolution of the
gluon fields is studied via the Classical Yang-Mills equations up to proper
time $\tau\approx 1$ fm/c for an $SU(2)$ evolving Glasma. Topological charge is
related to the gauge invariant $\bm E \cdot \bm B$ where $\bm E$ and $\bm B$
denote the color-electric and color-magnetic fields, while the chiral density
is produced via the chiral anomaly of Quantum Chromodynamics. We study how the
correlation lengths are related to the collision energy, and how the correlated
domains grow up with proper time in the transverse plane for a boost invariant
longitudinal expansion. We estimate the correlation lengths of both quantities,
that after a short transient results of the order of the typical energy scale
of the model, namely the inverse of the saturation scale. We estimate the
proper time for the formation of a steady state in which the production of the
chiral density in the transverse plane per unit rapidity slows down, as well as
the amount of chiral density that would be present at the switch time between
the Classical Yang-Mills evolution and the relativistic transport or hydro for
the quark-gluon plasma phase.
