From Power-Localized to Extended States in a Class of One-Dimensional Disordered Systems

We study a one-dimensional random Kronig-Penney model in the presence of a constant electric field. We rigorously prove for the first time the existence of a transition between a regime of extended states for large field and a regime of power-localized states for small field. There the large-distance behavior of the states is |x|^-α(F) with α(F)~C/F for small field F, confirming a numerical computation of Soukoulis et al.