Interaction of quasilocal harmonic modes and boson peak in glasses

Abstract

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 ${\omega }_b=(1.5\mathrm{}\pm 0.1){\omega }_d.$ At frequency ${\omega }_d$ the mean free path of the phonons l becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. 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.