QUASI-LOCALIZED SOUND EXCITATIONS IN DISORDERED-SYSTEMS

A theory of the low-frequency vibrational spectra in disordered system s is proposed and is based on accounting for small statistical fluctua tions of the sound velocity. Long-range quasilocalized sound excitatio ns of a circular nature are predicted. A circular excitation is locali zed during its lifetime inside an appropriate fluctuation that has the form of a thin tube bent into a ring. The density of states of such e xcitations estimated by the optimum fluctuation method depends exponen tially on the frequency. The existence of a characteristic frequency i s found at which the density of the quasilocalized states competes wit h that of phonons, providing a kind of anomaly in the total density of vibrational states. This frequency depends both on the correlation ra dius of the disorder and its amplitude. The theory predicts qualitativ ely a universal behavior of the density of vibrational states in vario us disordered systems possessing medium-range order.