On the theory of Boson peak in glasses

A universal mechanism of the Boson peak formation in glasses is proposed. The mechanism is based on the concept of interacting quasi-local oscillators. Even in the case of weak interaction the low-frequency spectrum becomes unstable. Due to anharmonicity the system undergoes a transition into a new stable configuration. As a result, below some characteristic frequency $\omega_c$, proportional to the typical strength of interaction, the renormalized density of states becomes a universal function of $\omega$ with a Boson peak feature, i.e. the reduced density of states $g(\omega)/\omega^2$ has a maximum at a frequency $\omega_b\ll\omega_c$. We derive an analytical form of this function.