Phonons in Glasses: Numerical Simulations and Phenomenological Theory

The phonon spectrum $\omega \left(k\right)$ 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.”