Rearrangement of the acoustic phonon spectrum in a one-dimensional disordered system with heavy isotope impurities

Abstract

The rearrangement of the acoustic phonon spectrum under the increase of isotope impurity concentration is studied in a one-dimensional system. The analysis is based on the method of the expansion of the single-particle Green's function in terms of clusters of the indirectly interacting impurity centers. It is demonstrated that the criterion for the validity of the coherent potential approximation (CPA) coincides exactly with the conventional Ioffe-Regel-Mott criterion. Approximate solutions for the dispersion relation and density of states are obtained for concentrations larger and smaller than the critical concentration of the spectrum rearrangement.