Why have the Vibrational Frequency Spectra of Disordered Chains Many Distinct Peaks?

By using the vector picture introduced previously, it is shown that disordered diatomic chains with sufficiently large mass-ratio have very strong tendency to have eigenfrequencies which are close to those of localized modes produced by several types of islands containing light atoms imbedded in a regular lattice composed of heavy atoms. This explains why the vibrational frequency spectra of disordered chains have in general very complicated structures with many well-defined peaks.