Interaction of quasilocal harmonic modes and boson peak in glasses

Abstract

The direct proportionality relation between the boson peak maximum in glasses, $ω_b$, and the Ioffe-Regel crossover frequency for phonons, $ω_d$, is established. For several investigated materials $ω_b = (1.5\pm 0.1)ω_d$. At the frequency $ω_d$ 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 $ω_b$ and $ω_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.