Low-frequency vibrations in a model glass

Previous simulation studies of localized low-frequency vibrational modes in a soft sphere glass are extended to larger samples. We find a boson peak in the spectral density and a maximum in the specific heat divided by ${\mathit{T}}^3$ similar to experiment. These maxima are caused by (quasi)localized vibrations. For finite frequencies these interact strongly with each other and with the extended phonons. This leads to an overdamping of the phonons around the boson peak and to a delocalization of the localized modes. A procedure to split the resulting modes into their bare constituents is presented. The bare localized modes are found to have a low-dimensional structure. The description in terms of the soft potential model is essentially verified. © 1996 The American Physical Society.