MULTIFRACTAL STATISTICS OF EIGENSTATES OF 2D DISORDERED CONDUCTORS

We have studied the manifestation of pre-localized states in the distr ibution of local amplitudes of wave functions of a 2D disordered metal . Although the distribution of comparatively small amplitudes obeys th e universal laws known from the random matrix theory, its large-amplit ude tails are non-universal and have a logarithmically-normal dependen ce. The inverse participation numbers calculated on the basis of the e xact form of the distribution function in the weak localization regime indicate multifractal behavior. Our calculation is based on the deriv ation of the non-trivial saddle-point of the reduced supersymmetric si gma-model.