Vibrational spectrum of disordered linear chain with light isotopic impurities. Region of the initial band Available to Purchase

The vibrational spectrum of disordered linear chains with light impurities of substitution is calculated within the region of the unperturbed band. The overall structure of the spectrum and the spectral shift function are determined. The results of a numerical calculation are compared with the known analytical expressions. The character of the statistical distribution of vibrational frequencies over different parts of the spectrum is investigated, and it is shown that at a sufficient impurity concentration in not-too-wide spectral intervals a completely random distribution of eigenfrequencies is realized. It is found that, with increasing concentration, sequences of minima and maxima arise with increasing clarity in the high-frequency half of the band, their positions being independent of the concentration and clumped towards the outer edge of the band. An expression giving the values of these special frequencies is found.