The vibrational density of states $D(\omega )$ of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye’s law, $D(\omega )\propto {\omega }^2$. In amorphous solids, phonons are damped, and at low frequency $D(\omega )$ comprises extended modes in excess over Debye’s prediction, leading to the so-called boson peak in $D(\omega )/{\omega }^2$ at ${\omega }_{\mathrm{bp}}$, and quasilocalized ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory, and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by quasilocalized modes acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids’ vibrational anomalies to elastic disorder and localized defects.

中文翻译：

---

非晶材料振动异常的统一描述

态的振动密度 $D(\omega )$固体控制它们的热和传输特性。在晶体中，低频模式是根据德拜定律在频率上分布的扩展声子，$D(\omega )\propto {\omega }^2$. 在无定形固体中，声子受到阻尼，并且在低频$D(\omega )$ 包括超出德拜预测的扩展模式，导致所谓的玻色子峰 $D(\omega )/{\omega }^2$ 在 ${\omega }_{\mathrm{基点}}$, 和准定位的。在这里，我们表明瑞利散射区中的玻色子峰和声子衰减是相关的，如相关波动弹性理论所暗示的那样，并且无定形材料可以被描述为均匀各向同性的弹性介质，被作为弹性异质性的准局域模式打断。我们的数值结果解决了将非晶固体的振动异常归因于弹性无序和局部缺陷的理论方法之间的冲突。