CHAOTIC AND CRITICAL FLUCTUATIONS IN SPECTRA OF DISORDERED SYSTEMS AT HIGHER DIMENSIONS

Abstract

The statistics of electron energy levels at the metal-insulator transition for hypercubic lattices with spatial dimensionality higher than 3 is investigated. The energy level distribution is shown to deviate from the results of the random-matrix theory in comparison with three-dimensional systems and tends towards Poisson limit for uncorrelated spectra. By applying the finite size scaling scenario, we calculate the full probability function of the level number in the energy interval of a given width.