Vibrations at the boson peak: random- and coherent-phase contributions

Analysis of the dynamic structure factor, S(Q, E), measured by means of inelastic neutron and x-ray scattering, for vibrations around the boson peak in glasses, demonstrates the presence of coherent- and random-phase contributions. It is found that systems with strong boson peaks have larger random-phase contributions to S(Q, E). The results of the analysis are explained in terms of a model which relates the boson peak to scattering of acoustic-like vibrations by spatial fluctuations of elastic constants. Higher amplitude of the fluctuations leads to a higher boson peak and a larger random-phase contribution.