Anharmonicity, vibrational instability and Boson peak in glasses

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency ${\omega }_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter – the Boson peak frequency, ${\omega }_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto {\omega }^4$ at low frequencies and linear in $\omega$ in the interval ${\omega }_b\ll \omega \ll {\omega }_c$. Our results are in an excellent agreement with recent experimental studies.