QUASI-LOCALIZED STATES IN DISORDERED METALS AND NONANALYTICITY OF THELEVEL CURVATURE DISTRIBUTION FUNCTION

It is shown that the quasilocalized stales in weakly disordered system s can lead to the nonanalytical distribution of level curvatures. In 2 D systems the distribution function P(K) has a branching point at K = 0, while in quasi-ID systems the nonanalyticity is very weak and in 3D metals it is absent. It was shown earlier within the similar saddle-p oint method 1-hat For weak disorder the wave functions possess a (weak ) multifractality only in 2D systems. This allows us to conjecture tha t the branching in P(K) at K = 0 is a generic feature of all critical eigenstates with multifractal statistics. A relationship between the b ranching power and the fractal dimensionality D-2 is suggested.