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

Abstract

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 ${|x|}^{\ensuremath{-}\ensuremath{\alpha}(F)}$ with $\ensuremath{\alpha}(F)\ensuremath{\sim}\frac{C}{F}$ for small field $F$, confirming a numerical computation of Soukoulis et al.