Descete Spectrum of Delocalized States in One-Dimensional Random Potensial

TL;DR

This paper demonstrates the existence of delocalized states in certain one-dimensional disordered systems, challenging the traditional view that all such states are localized, and highlights their role as energy filters.

Contribution

It reveals that delocalized states can exist in specific one-dimensional models, expanding understanding beyond the conventional localization theorem.

Findings

Delocalized states exist in a broad class of 1D disordered models.

The set of delocalized states is limited and consistent with refined localization theorems.

Systems can act as energy filters for electrons.

Abstract

It is well known$^{1,2}$ that in one-dimensional disordered system all states of electrons (or any other exitations) are localized. In this letter it is shown that delocalized states exist in a rather broad class of of simple models, but a set of delocalized states is not too great, and it does not contradict this theorem in more precize form$^{2,3}$. These systems can be considered as filters in energy for electrons.