Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder

Abstract

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. We present a tensorial replica field-theoretic derivation based on heterogeneous or fluctuating elasticity (HE), which shows that long-range (power-law) spatial correlations of the elastic constants, is the origin of the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids. We also consider the case of zero spatial fluctuations in the elastic constants, and of power-law decaying fluctuations in the internal stresses. Also in this case the logarithmic enhancement to the Rayleigh scattering law can be derived from the proposed tensorial HE framework.

References in corpus (3)

• Acoustic excitations and elastic heterogeneities in disordered solids
• Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling
• Impact of elastic heterogeneity on the propagation of vibrations at finite temperatures in glasses

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• Physics of Phonon-Polaritons in Amorphous Materials
• Novel elastic instability of amorphous solids in finite spatial dimensions
• Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity