非晶态固体中声子输运与连通性的标度
Scaling of phononic transport with connectivity in amorphous solids
摘要：
以随机弹簧网络为模型系统，从理论上研究了协调对输运的影响。一个有效的介质近似计算的振动模式的态密度，它们的能量扩散率（运输的光谱测量）和它们的空间相关性的网络协调$z$是不同的。在这些网络失去刚性的情况下，获得了作为$z\to z_c$的临界行为。在某些频率$ω^*\sim z-z_c$处，出现从模式为平面波状的区域到扩展但强散射模式区域的急剧交叉，该频率不符合Ioffe-Regel准则。在$ω^*$以上，态密度和扩散率几乎不变。这些结果同意显着最近的数值观测排斥粒子附近的干扰阈值\cite{ning}。分析进一步预测，表征散射模式的位移的相关性的长度尺度随频率衰减为$1/\sqrtω$，而对于$ω<<ω^*$瑞利散射被发现与散射长度$l_s\sim (z-z_c)^3/ω^4$。有人认为，这种描述适用于石英玻璃，它比较以及与热导率数据，并在颗粒物质中的横向超声传播。
英文摘要：
The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination $z$ is varied. Critical behaviors are obtained as $z\to z_c$ where these networks lose rigidity. A sharp cross-over from a regime where modes are plane-wave-like toward a regime of extended but strongly-scattered modes occurs at some frequency $ω^*\sim z-z_c$, which does not correspond to the Ioffe-Regel criterion. Above $ω^*$ both the density of states and the diffusivity are nearly constant. These results agree remarkably with recent numerical observations of repulsive particles near the jamming threshold \cite{ning}. The analysis further predicts that the length scale characterizing the correlation of displacements of the scattered modes decays as $1/\sqrtω$ with frequency, whereas for $ω<<ω^*$ Rayleigh scattering is found with a scattering length $l_s\sim (z-z_c)^3/ω^4$. It is argued that this description applies to silica glass where it compares well with thermal conductivity data, and to transverse ultrasound propagation in granular matter.
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