Dynamics of a disordered monatomic solid with continuous distribution of force constants

The average local-information transfer approximation (ALITA) Green's function 〈G→Q({ω})〉 (where Q and {ω} are the wave vector and the frequency, respectively) and related longitudinal (L) and transverse (T) dispersion curves, frequency spectrum and neutron inelastic scattering (NIS) cross section have been calculated for a monatomic solid, disordered with respect to interatomic coupling and atomic configuration. Rectangular, elliptic, and Lorentz distributions of the self-force constants in the nearest-neighbor central-force model have been assumed. It has been found that the frequency spectrum of such a system is dominated by a huge peak at the average Einstein frequency due to the T curve, and a bump at lower frequency representing the first minimum in the L curve. Force disorder manifests itself in extending the range of frequencies and in rounding off the details of the spectrum corresponding to configuration disorder. Besides, the plane-wave deformations with wave vectors in certain ``Q gaps'' cannot contribute to normal modes of vibration in disordered solids. The NIS cross section at large momentum transfer {}Q leads directly to the spectrum of Einstein frequencies. If this spectrum has a sharp edge at 0, then essential deviations from the Debye type of frequency spectrum and from the T³ law for vibrational specific heat at low temperatures do appear.