Barlow填料的超一致序度量
Hyperuniformity Order Metric of Barlow Packings
摘要：
超均匀性的概念是研究自然科学和数学系统中大尺度密度涨落的有用工具。人们可以通过使用超均匀性序度量$\barΛ$来对一类超均匀系统进行排序，这取决于它们抑制长程密度涨落的能力。我们应用这个顺序度量的Barlow包装，这是无限退化densitivepackings的相同的刚性球体，区分它们的堆叠几何形状，包括通常已知的fcc晶格和六方晶系。“隐形堆叠”定理意味着这些填充都是隐形超均匀的，一种强类型的超均匀性，涉及到波矢$K$的散射抑制。我们描述了三个类的Barlow包装，两个无序类和小周期包装的几何。此外，我们还计算了所有Barlow填充的$K$的下界.我们计算$\barΛ$的上述三类Barlow包装，并发现，一个非常好的近似，它是线性的fcc类集群的分数，采取的最低顺序hcp和最有序fcc之间的值。这意味着所有Barlow填料的$\barΛ$主要由局部簇几何形状控制。这些结果表明了各向异性堆垛层错的特殊性质，为进一步研究各向异性有序度和超均匀性提供了动力。
英文摘要：
The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric $\barΛ$. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity which involves the suppression of scattering up to a wavevector $K$. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on $K$ for all Barlow packings. We compute $\barΛ$ for the aforementioned three classes of Barlow packings and find that to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the $\barΛ$ of all Barlow packings is primarily controlled by the local cluster geometry. These results indicate the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.
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