Phonons in glasses: Numerical simulations and phenomenological theory

The phonon spectrum omega(k) of a model glass is investigated by classical molecular dynamics. While the longitudinal branch looks like one of a crystal, the transverse branch saturates at an almost k-independent characteristic frequency omega(c), which tends to zero at the glass transition temperature. These results confirm an earlier picture in which a glass is a solid containing liquid ''pockets'' of finite sizes. For omega > omega(c), the transverse phonons are absorbed by the resonant modes of the finite clusters, the latter being responsible for the ''boson peak.''