论文标题
具有长距离幂律相关性弹性的无定形固体状态的振动密度
Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
论文作者
论文摘要
为了确定无序固体的状态$ d（ω）$的振动密度，得出了基于弹性常数（或等效地在内部应力中）的振动激发理论。该结果提供了无定形材料中玻色子峰的第一个预测，其中内部应力（或弹性常数）中的空间相关性是幂律形式的，在实验系统中通常是这种情况，从而导致（Rayleigh）声子衰减的对数增强。预计在3D中玻色子峰附近的频率的频率中，预计将对形式的$ \ sim-Ω^{2} \lnΩ$进行对数校正。此外，该理论提供了低频区域中状态密度的缩放定律，包括3D中的$ \simΩ^{4} $制度，并提供有关玻色子峰强度如何取决于弹性常数或内部压力中波动势力衰减的强度的信息。分析表达式也针对纵向激发的动态结构因子得出，其中包括对数校正因子，并提供了数值计算，以支持理论中使用的假设。
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 $D(ω)$ 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 logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $\sim -ω^{2}\lnω$ 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 $\simω^{4}$ 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.
