Statistics of Wave Functions in Disordered and in Classically Chaotic Systems

Abstract

We consider the statistics of wave function intensities in disordered and classically chaotic systems. We present numerical results for the two-dimensional tight-binding Anderson model of localization and for the hydrogen atom in a strong magnetic field. At low disorder or strong classical chaos, respectively, we find extended states which show a Porter-Thomas distribution of intensities according to the universal predictions of random matrix theory. Localization due to disorder or weakly unstable regions in classical phase space causes characteristic deviations from universality.