Phonon excitations in multicomponent amorphous solids

The method of two-time temperature-dependent Green's functions is used to investigate phonon excitations in multicomponent amorphous solids. The equation obtained for the energy spectrum of the phonon excitations takes into account the damping associated with scattering of phonons by structure fluctuations. The quasicrystal approximation is considered, and as an example explicit expressions are obtained for the case of a two-component amorphous solid for the frequencies of the acoustical and optical modes and for the longitudinal and transverse velocities of sound. The damping is investigated.