Multifractal statistics of eigenstates of 2D disordered conductors

We have studied the manifestation of pre-localized states in the distribution of local amplitudes of wave functions of a 2D disordered metal. Although the distribution of comparatively small amplitudes obeys the universal laws known from the random matrix theory, its large-amplitude tails are non-universal and have a logarithmically-normal dependence. The inverse participation numbers calculated on the basis of the exact form of the distribution function in the weak localization regime indicate multifractal behavior. Our calculation is based on the derivation of the non-trivial saddle-point of the reduced supersymmetric σ-model.