Key points are not available for this paper at this time.
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 ρ∝Im G (E, x, x), with the Hamiltonian H describing the motion of a quantum particle in a d-dimensional disordered system. Corresponding distributions are related to a function which plays the role of an order parameter for the Anderson metal-insulator transition. When the system can be described by a nonlinear σ-model, the distribution 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-power-like critical behavior obtained earlier for effectively infinite-dimensional models. For any finite dimension d < ∞ the critical behavior is demonstraied to be of the conventional power-law type wilh d = ∞ playing the rote of an upper critical dimension.
Mirlin et al. (Sun,) studied this question.