STATISTICAL PROPERTIES OF ONE-POINT GREEN-FUNCTIONS IN DISORDERED-SYSTEMS AND CRITICAL-BEHAVIOR NEAR THE ANDERSON TRANSITION

We investigate the statistics of local Green functions G(E, x, x) = [x \(E-H)-1\x], in particular of the local density of states rho is-propo rtional-to Im G (E, x, x), with the Hamiltonian H describing the motio n of a quantum particle in a d-dimensional disordered system. Correspo nding distributions are related to a function which plays the role of an order parameter for the Anderson metal-insulator transition. When t he system can be described by a nonlinear sigma-model, the distributio n is shown to possess a specific <<inversion>> symmetry. We present an analysis of the critical behavior near the mobility edge that follows from the abovementioned relations. We explain the origin of the non-p ower-like critical behavior obtained earlier for effectively infinite- dimensional models. For any finite dimension d < infinity the critical behavior is demonstrated to be of the conventional power-law type wit h d = infinity playing the role of an upper critical dimension.