The problem of localization in one-dimensional disordered systems (A new approach)

The theorem proved in 1951 by Molchanov [15] is utilized to investigate the problem of localization of one-electron states in one-dimensional disordered systems. The theorem permits to treat the problem in a general way and establishes a new criterion of localization, which is based on the asymptotic features of a random potential. It is shown that in the case of diagonal disorder the theorem does not lead to new results; namely, all the states are found to be localized. However, in the case of structural disorder it follows from the theorem that all the states can be delocalized under relatively weak restrictions.