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The dynamics of a soft sphere model glass, studied by molecular dynamics, isinvestigated. The vibrational density of states divided by $\omega^2$ shows apronounced boson peak. Its shape is in agreement with the universal formderived for soft oscillators interacting with sound waves. The excessvibrations forming the boson peak have mainly transverse character. From thedynamic structure factor in the Brillouin regime pseudo dispersion curves arecalculated. Whereas the longitudinal phonons are well defined up to the pseudozone boundary the transverse ones rapidly get over-damped and go through theIoffe-Regel limit near the boson peak frequency. In the high $q$ regimeconstant-$\omega$ scans of the dynamic structure factor for frequencies aroundthe boson peak are clearly distinct from those for zone boundary frequencies.Above the Brillouin regime, the scans for the low frequency modes followclosely the static structure factor. This still holds after a deconvolution ofthe exact harmonic eigenmodes into local and extended m odes. Also thestructure factor for local relaxations at finite temperatures resembles thestatic one. This semblance between the structure factors mirrors the collectivemotion of chain like structures in both low frequency vibrations and atomichopping processes, observed in the earlier investigations

Vibrations and relaxations in a soft sphere glass: boson peak and structure factors