Abstract.

A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D(\(\omega\)) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form \( \sim -\omega^{2}\ln\omega\) is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a \( \sim\omega^{4}\) regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory.

Graphical abstract

中文翻译：

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弹性与远距离幂律相关的无定形固体的状态振动密度

摘要。

推导了一种基于弹性常数（或等效地，内部应力）中幂律空间相关性的振动激励理论，以确定无序固体状态D（\（\ omega \））的振动密度。结果提供了对非晶态材料中玻色子峰的第一个预测，其中内部应力（或弹性常数）的空间相关性呈幂律形式，这在实验系统中经常出现，从而导致（Rayleigh）的对数增强声子衰减。\（\ sim-\ omega ^ {2} \ ln \ omega \）形式的对数校正对于3D玻色子峰附近的频率，预计会在减少的过量DOS图中发生。此外，该理论提供了低频区域中状态密度的缩放定律，包括3D中的\（\ sim \ omega ^ {4} \）体制，并提供了有关玻色子峰强度如何取决于强度的信息。弹性常数或内应力波动的幂律衰减曲线。还导出了纵向激励的动态结构因子的解析表达式，其中包括对数校正因子，并给出了支持理论中所用假设的数值计算。

图形概要