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 omega(c), 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 omega(b) which is a function of interaction strength. The excess of the DOS over the Debye value is proportional toomega(4) at low frequencies and linear in omega in the interval omega(b)<<omega<<omega(c). Our results are in an excellent agreement with recent experimental studies.