Soft-mode related origin of the boson peak and acoustic-phonon broadening in glasses

We study the origin of the boson peak and an associated mechanism for acoustic-phonon broadening (below the peak) in glasses exhibiting a high-frequency sound above the peak. The origin is related to the Ioffe–Regel crossover for inelastic (resonant) scattering of acoustic phonons from harmonic soft-mode vibrations. The broadening mechanism is due to the resonant interaction of a harmonic soft-mode vibration with acoustic phonons, which results in the resonant scattering. We find that the associated width of the phonon is independent of temperature and is characterized by a power-law frequency dependence with the exponent varying from $\varkappa=2$ just below the boson peak to $\varkappa=4$ at lower frequencies. The dependences seem to partly agree with some recent experimental data for the glasses under consideration.