On the problem of non-transport of electrons in disordered systems (Anderson localization)

Abstract

The problem of non-transport (Anderson localisation) in cellularly disordered systems is well known to be related to the question of convergence of the Brillouin Wigner perturbation expansion for self-energy involving random energy denominators. In this preliminary communication an explicit criterion for the absolute convergence in the probability sense, of a partial series, has been obtained in terms of the width Δ of the rectangular distribution of the random site-energies and the band width W. The partial series considered involves only terms with non-repeating site indices.