Phase correlations of localized electronic wave functions in disordered one- and two-dimensional systems

We investigate the phase correlations of the localized eigenfunctions of the Anderson hamiltonian with diagonal disorder. For the ld-case we show analitically that long-range phase correlations exist for eigenstates near the band edges, whereas they disappear near the band centre. Our numerical calculations confirm the analytical results for the ld-case and show also, that the behavior of the phase correlations is similar in 2d-systems.