VIBRATIONAL ANOMALIES AND PHONON LOCALIZATION IN GLASSES

A self-consistent effective-medium scheme for describing sound propagation in glasses developed recently by the authors is simplified by a factorization approximation. This approximation allows for a schematical distinction between longitudinal and transverse modes. As in the previous ''scalar'' description of sound propagation in glasses a crossover from nearly free sound propagation at low frequencies to strongly damped motion at higher frequencies is found and related to vibrational and thermal anomalies in glasses in the intermediate frequency/temperature regime. Using the self consistent current relaxation theory we discuss whether or not the modes above the crossover are localized. The mean free path in the non-overdamped regime is discussed in relation to other approaches based on Rayleigh scattering formulae.