A numerical study of wave-function and matrix-element statistics in the Anderson model of localization

We have calculated wave functions and matrix elements of the dipole operato r in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In par ticular, we have considered two cases. First, we have studied the fluctuati ons as an external Aharonov-Bohm flux is varied. Second, we have considered the influence of incipient localization. In both cases, the statistical pr operties of the eigenfunctions are non-trivial, in that the joint probabili ty distribution function of eigenvalues and eigenvectors does no longer fac torize. We report on detailed comparisons with analytical results, obtained within the non-linear sigma model and/or the semiclassical approach.