Elastic moduli fluctuations predict wave attenuation rates in glasses

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 Γ(ω) in the low-frequency limit (ω → 0) and 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, Γ(ω) ∼ γ ω^-d+1, where γ = γ(V_c) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume V_c that remains debated. Here, using extensive computer simulations, we show that Γ(ω) ∼ γω³ is asymptotically satisfied in two dimensions ( -d = 2) once γ is interpreted in terms of ensemble-rather than spatial-averages, where V_c is replaced by the system size. In doing so, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal ω⁴ 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.