Elastic moduli fluctuations predict wave attenuation rates in glasses

TL;DR

This study demonstrates that wave attenuation in 2D glasses follows a predicted scaling law related to elastic moduli fluctuations, linking microscopic disorder to macroscopic wave behavior through extensive simulations.

Contribution

It confirms the Fluctuating Elasticity Theory's prediction of Rayleigh scattering scaling in glasses by interpreting elastic moduli fluctuations via ensemble averages rather than spatial ones.

Findings

Wave attenuation scales as requency^3 in 2D glasses.

Ensemble statistics of elastic moduli are anomalous and connected to soft mode density.

Results provide a benchmark for coarse-grained elastic moduli distributions.

Abstract

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate $\Gamma(\omega)$ in the low-frequency limit ($\omega\!\to\!0$), and on its dependence on glass history and properties. A theoretical framework -- termed Fluctuating Elasticity Theory (FET) -- predicts low-frequency Rayleigh scattering scaling in $d$ spatial dimensions, $\Gamma(\omega)\!\sim\!\gamma\,\omega^{d+1}$, where $\gamma\!=\!\gamma(V_{\rm c})$ quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume $V_{\rm c}$ that remains debated. Here, using extensive computer simulations, we show that $\Gamma(\omega)\!\sim\!\gamma\,\omega^3$ is asymptotically satisfied in two dimensions ($d\!=\!2$) once $\gamma$ is interpreted in terms of ensemble -- rather than spatial -- averages, where $V_{\rm c}$ is replaced by the system size. In so doing, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal $\omega^4$ density of states of soft quasilocalized modes. These results not only strongly support FET, but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.