Charge transfer and anderson localization in one-dimensional finite-size disordered systems

Abstract

The metal–insulator transition in finite one-dimensional lattices with diagonal disorder is considered. Although the true phase transition does not occur in such systems, a conditional criterion can be introduced to distinguish the regions of localization and delocalization of eigenvectors and wave functions, depending on the degree of disorder W. A relationship between the degree of disorder W and the characteristic length separating the localized and delocalized states is obtained: with high accuracy, ξ_cr ~ W^–2. The calculations are performed by integrating the evolutional Schrodinger equations and through analyzing the spectral properties of the corresponding random matrices. The probability of charge transfer is estimated within the framework of a simple model of DNA.