Anharmonicity, vibrational instability, and the Boson peak in glasses

We show that a vibrational instability of the spectrum of weakly interacting quasilocal 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 vc , proportional to the strength of interaction. The DOS of the new 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 vb which is a function of interaction strength. The excess of the DOS over the Debye value is }v at low frequencies and linear in v in the interval vb!v!vc . Our results are in an excellent agreement with recent experimental studies.