SPECTRAL CORRELATIONS FROM THE METAL TO THE MOBILITY EDGE

We have studied numerically the spectral correlations in a disordered 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. We also find numerically the diffusive corrections for the number variance [delta n(2)(s)] predicted by Al'tshuler and Shklovskii. 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'\ much greater than 1, it is found to decrease as a power law R(s, s') similar to -c/\s - s'\(2-gamma) with c similar to 0.041 and gamma similar to 0.83, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor <(K)over tilde (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<(K)over tilde (0)>[n], where <(K)over tilde (0)> is the limit of the form factor for t --> 0.