Phonons in Glasses: Numerical Simulations and Phenomenological Theory.

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The phonon spectrum $\ensuremath{\omega}(k)$ 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 ${\ensuremath{\omega}}_{c}$, 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 $\ensuremath{\omega}>{\ensuremath{\omega}}_{c}$, the transverse phonons are absorbed by the resonant modes of the finite clusters, the latter being responsible for the ``boson peak.''