Model calculations for vibrational properties of disordered solids and the"boson peak"

It is demonstrated that a disordered system of coupled classical harmonic o scillators with a continuous distribution of coupling parameters exhibits g enerally a low-frequency enhancement ("boson peak") of the density of state s, as compared with the Debye law. This phenomenon is most pronounced if th e system is close to an instability. This is shown by means of a scalar mod el on a simple cubic lattice. The force constants are assumed to fluctuate from bond to bond according to a Gaussian distribution which is truncated a t its lower end. The model is solved for the density of states and the one- phonon dynamic structure factor S(q,omega) by applying the two-site coheren t potential approximation (CPA). The results for the density of states are in very good agreement with a numerical evaluation of the same model. (C) 1 999 Elsevier Science B.V. All rights reserved.