Analytical theory of enhanced logarithmic Rayleigh scattering in amorphous solids

The damping or attenuation coefficient of sound waves in solids due to impurities scales with the wavevector to the fourth power, also known as Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced by a logarithmic factor although computer simulations offer conflicting conclusions regarding this enhancement and its microscopic origin. With tensorial replica field strategy, a theoretic derivation based on heterogeneous elasticity suggests that the logarithmic enhancement to Rayleigh scattering of phonons might be ascribed to long-range (power-law) power law decay in spatial elastic disorder in amorphous solids. Further, the density of states (DOS) associated with self-consistent equations of self-energy in the model exhibit power d+1 decay in low frequency regime, supporting the evidence of numerical simulation in sound waves.