Elastic moduli fluctuations predict wave attenuation rates in glasses

The disorder-induced attenuation of elastic waves is central to the universal lowerature 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.