- m at . d is - n n ] 1 6 Ju l 1 99 9 Scattering of plane - wave atomic vibrations in disordered structures

A theoretical analysis of the scattering of plane-wave atomic excitations in disordered solids has been made in terms of the spectral densities. Hybridization between transverse and longitudinal waves of approximately the same frequency is demonstrated. The analytic results agree well with the results obtained from computer simulation for a toy linear zigzag chain model and a model of vitreous silica constructed by molecular dynamics. Propagation of classical plane waves in random scattering media has attracted a lot of theoretical and experimental attention in recent years [1,2]. The phenomena of wide interest include weak localization [1,2], Anderson localization [3], phonon localization [4–6] and related behaviour of plane waves in the Ioffe-Regel crossover region [7] separating weakly and strongly scattered waves [8,9]. Vibrational plane waves propagate well in disordered structures in the long-wavelength limit, ka ≪ 1, with k the wavevector and a a measure of the microscopic scale of the structure (being of the order of interatomic distances), when the atomic structure behaves as an elastic continuum and disorder on the microscopic level is not of great importance. The situation is changed with decreasing wavelength and, on the microscopic scale, disorder becomes important and the wavevector is no longer a good quantum value [10–17]. In the investigation of the propagation of the plane-wave vibrational excita-tions in disordered structures, different decay channels have been suggested to explain their attenuation: (i) disorder-induced channels [18–22], (ii) anharmonic channels [20] and (iii) channels involving two-level systems [23–26]. The anhar-monic channels are strongly enhanced with increasing temperature, particularly at temperatures comparable with the glass-transition temperature, T g ∼ 10 3 K. In