An analysis of the fine structure in the main band of a disordered chain with dilute light impurity concentrations

Abstract

Abstract The main band of a disordered binary chain is studied, using Dean's method of negative mode counting, Schmidt's method of functional equation and an approximate theory of Wu. It is found that even for dilute light impurity concentrations, the main band is not smooth as previously believed, but has fine structure. By comparing the results of these calculations, the nature of the construction of the frequency spectrum in the form of a histogram is discussed. The truncation scheme in the approximate theory of Wu is also examined.