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

## TL;DR

This paper develops a tensorial field-theoretic framework to explain the logarithmic enhancement of Rayleigh scattering in amorphous solids, attributing it to long-range elastic correlations and stress fluctuations.

## Contribution

It introduces a novel tensorial replica field-theoretic approach that links long-range elastic correlations to Rayleigh scattering enhancement in amorphous materials.

## Key findings

- Logarithmic enhancement arises from power-law spatial correlations of elastic constants.
- The framework applies to both elastic constant fluctuations and internal stress fluctuations.
- The theory aligns with conflicting simulation results and clarifies microscopic origins.

## 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.