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A hallmark of glasses is an excess of low-frequency, nonphononic vibrations,in addition to phonons. It is associated with the intrinsically nonequilibriumand disordered nature of glasses, and is generically manifested as a THz peak-- the boson peak -- in the ratio of the vibrational density of state (VDoS)and Debye's VDoS of phonons. Yet, the excess vibrations and the boson peak arenot fully understood. Here, using reanalysis of experimental data, extensivecomputer simulations and a mean-field model, we show that the nonphononic partof the VDoS itself features both a universal power-law tail and a peak,entirely accounted for by quasi-localized nonphononic vibrations, whoseexistence was recently established. We explain the mild variation of the peak'sfrequency and magnitude with glasses' thermal history, along with the strongvariation of the power-law tail. We also show that modes that populate thepeak's region feature many coupled quasi-localized nonphononic vibrations, whentheir spatial structure is considered. Our results provide a unified physicalpicture of the low-frequency vibrational spectra of glasses, and in particularelucidate the origin, nature and properties of the boson peak.

The boson peak in the vibrational spectra of glasses