Localized states in disordered systems as bound states in potential wells

Abstract

The equivalence between localized states in disordered $d$-dimensional systems and bound states in local potential wells (or local potential fluctuations) in $d$-dimensional space is tested against numerical data. The agreement is found to be satisfactory. A new criterion for the onset of localization is deduced. It reduces to Mott's criterion at the center of the band but it differs qualitatively from Mott's picture when the mobility edge is near the band edges.