  The dynamics of a soft sphere model glass, studied by molecular dynamics, is
investigated. The vibrational density of states divided by $\omega^2$ shows a
pronounced boson peak. Its shape is in agreement with the universal form
derived for soft oscillators interacting with sound waves. The excess
vibrations forming the boson peak have mainly transverse character. From the
dynamic structure factor in the Brillouin regime pseudo dispersion curves are
calculated. Whereas the longitudinal phonons are well defined up to the pseudo
zone boundary the transverse ones rapidly get over-damped and go through the
Ioffe-Regel limit near the boson peak frequency. In the high $q$ regime
constant-$\omega$ scans of the dynamic structure factor for frequencies around
the boson peak are clearly distinct from those for zone boundary frequencies.
Above the Brillouin regime, the scans for the low frequency modes follow
closely the static structure factor. This still holds after a deconvolution of
the exact harmonic eigenmodes into local and extended m odes. Also the
structure factor for local relaxations at finite temperatures resembles the
static one. This semblance between the structure factors mirrors the collective
motion of chain like structures in both low frequency vibrations and atomic
hopping processes, observed in the earlier investigations.
