Frequency Spectrum of a Disordered One-Dimensional Lattice

Abstract

The frequency spectrum of a disordered one‐dimensional lattice is calculated via an investigation of the phonon propagator. The spectrum is evaluated in detail for a low concentration of light impurities inserted at random along a linear chain. It is found that an impurity band occurs near the frequency of the local mode. Higher‐order effects resulting from clusters of impurities are calculated and discussed.