Size effects and quasilocalized vibrations

The existence of localized vibrations at low frequencies in glasses and the notion and the properties of quasilocalized vibrations (QLVs) in glasses have been debated in the recent literature. By clarifying the main features of the QLVs and of the low-frequency vibration in model systems (a defect lattice and a Lennard-Jones glass in the harmonic approximation) we reach the conclusions, firstly, that truly localized modes are confined to the very-high-frequency tail and to gaps of the vibrational spectrum, secondly, that the QLVs are actually present at low frequencies in glasses, thirdly, that the QLVs are modes that involve all the atoms of the system (they are extended) but that they have few nearby atoms that carry a large fraction of the vibrational energy and, fourthly, that they are not a trivial mixing of extended and localized harmonic eigenmodes but rather appear to be an independent species of modes.