Acoustic-phonon spectrum rearrangement in a one-dimensional system with mass disorder

Abstract

We have investigated the anomalous rearrangement of the acoustic-phonon spectrum in a one-dimensional disordered system with increasing the heavy substitutional impurity concentration. The analysis shows that the anomalous spectrum rearrangement bears certain features of the normal cross-type spectrum rearrangement for the impurity concentration exceeding a certain concentration, the so-called second critical concentration c(s). Numerical simulation results for randomly disordered chains confirm the proposed criterion for the validity of the coherent potential approximation.