LOCALIZATION PROPERTIES OF KRONIG-PENNEY INCOMMENSURATE POTENTIALS

By means of the renormalization approach we study the localization properties of a one-dimensional system of δ-like potential barriers, whose heights are modulated incommensurately with respect to their separation. We show how to distinguish different types of localized states present in the spectrum. Our study shows that in the case of slowly varying potential heights, the Lyapunov coefficient of exponentially localized states approaches zero linearly in correspondence to energies where a transition to power-law localized states is present. A second transition to extended states is then observed. The consequences on the transmittivity of the system are described.