Exact diagonalization study of rare events in disordered conductors

We determine the statistical properties of wave functions in disordered qua ntum systems by exact diagonalization of one-, two-, and quasi-one-dimensio nal tight-binding Hamiltonians. In the quasi-one-dimensional case we find t hat the tails of the distributions of wave-function amplitudes are describe d by the nonlinear sigma model. In two dimensions, the tails of the distrib ution functions are consistent with a recent prediction based on a direct o ptimal fluctuation method.