  We have studied numerically the spectral correlations in a metallic phase and
at the metal-insulator transition. We have calculated directly the two-point
correlation function of the density of states $R(s,s')$. In the metallic phase,
it is well described by the Random Matrix Theory (RMT). For the first time, we
also find numerically the diffusive corrections for the number variance
$<\delta n^2(s)>$ predicted by Al'tshuler and Shklovski\u{\i}. At the
transition, at small energy scales, $R(s-s')$ starts linearly, with a slope
larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to
decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-\gamma}$ with $c \sim
0.041$ and $\gamma \sim 0.83$, in good agreement with recent microscopic
predictions. At the transition, we have also calculated the form factor $\tilde
K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance
contains two terms $<\delta n^2(s) >= B < n >^\gamma + 2 \pi \tilde K(0)< n >
where $\tilde{K}(0)$ is the limit of the form factor for $t \to 0$.

Condensed Matter