Anharmonic elasticity theory for sound attenuation in disordered solids with fluctuating elastic constants

Using anharmonic elasticity theory in the presence of spatially fluctuating elastic constants we derive a self-consistent theory for sound attenuation in disordered solids. In the low-frequency regime (below the boson peak frequency) we obtain a sound attenuation law proportional to T omega(2), where T is the temperature and omega is the frequency. Together with the usual Rayleigh scattering mechanism this yields a crossover of the Brillouin linewidth from a omega(2) to a omega(4) regime. The cross-over frequency is fully determined by the boson peak frequency and the temperature. For network glasses like SiO2 at room temperature this crossover is predicted to be situated one order of magnitude below the boson peak frequency.