Kapteijns Geert, Richard David, Bouchbinder Eran, Lerner Edan
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands.
Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel.
J Chem Phys. 2021 Feb 28;154(8):081101. doi: 10.1063/5.0038710.
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, where γ = γ(V) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume V that remains debated. Here, using extensive computer simulations, we show that Γ(ω) ∼ γω is asymptotically satisfied in two dimensions ( -d = 2) once γ is interpreted in terms of ensemble-rather than spatial-averages, where V 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 ω 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.
无序诱导的弹性波衰减是玻璃普遍低温特性的核心。近期文献对于低频极限（ω→0）下波衰减率Γ(ω)的标度及其对玻璃历史和性质的依赖性存在相互矛盾的观点。一个名为波动弹性理论（FET）的理论框架预测了在d维空间中低频瑞利散射标度，即Γ(ω) ∼ γω，其中γ = γ(V)量化了弹性模量的粗粒化空间涨落，涉及一个仍存在争议的关联体积V。在此，通过广泛的计算机模拟，我们表明一旦γ用系综平均而非空间平均来解释，其中V被系统尺寸取代，在二维（d = 2）中Γ(ω) ∼ γω渐近成立。在此过程中，我们还确定了弹性模量的有限尺寸系综统计是反常的，并且与软准局域模的通用ω态密度相关。这些结果不仅有力地支持了FET，而且为弹性模量空间分布的粗粒化方法所产生的统计提供了一个严格的基准。
