Interaction of quasilocal harmonic modes and boson peak in glasses

The direct proportionality relation between the boson peak maximum in glasses, ${\omega }_b$, and the Ioffe-Regel crossover frequency for phonons, ${\omega }_d$, is established. For several investigated materials $\omega_b = (1.5\pm 0.1)\omega_d$\mathrm{.}Atthefrequency$\omega_d$ the mean free path of the phonons $l$ becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between ${\omega }_b$ and ${\omega }_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.