论文标题
最近的邻居功能，用于无序的隐形高分多粒子系统
Nearest-Neighbor Functions for Disordered Stealthy Hyperuniform Many-Particle Systems
论文作者
论文摘要
$ \ mathbb {r}^d $中的无序隐形多粒子系统是抑制单个散射事件的异国情调状态，可用于围绕相互空间中的有限的波数范围。我们得出了无序隐秘系统最近邻里功能的分析公式。首先，我们分析基于伪硬质的Ansatz的渐近小$ r $ $ $ $ $ $ $近近似值和边界表达式。然后，我们确定需要多少个标准的$ n $ - 点相关功能来确定最近的邻居功能，并发现有限的数字就足够了。通过理论和计算方法，我们将这些功能对无序隐形系统的巨大$ r $行为与属于晶格的人进行了比较。这种有序和无序的隐身系统具有有限的孔尺寸。但是，我们发现临界孔大小的方法可能在数量上有所不同。我们认为，找到接近临界孔大小的孔的概率应作为一个功率定律，指数仅取决于有序系统的空间尺寸$ d $，但是对于无序系统而言，这种概率差异更快。这意味着接近临界孔大小的孔在无序系统中稀有。在无序系统中观察大孔的罕见性在对临界孔大小附近的最近的邻居分布进行采样时，造成了很大的数值困难。这激发了对有效抽样的新计算方法的需求，也需要新的理论方法的发展。我们还设计了一个简单的分析公式，该公式在所有$ r $的情况下准确地描述了这些系统。这些结果为无序，无限制制度中隐身系统最近邻里功能的分析描述奠定了基础。
Disordered stealthy many-particle systems in $\mathbb{R}^d$ are exotic states of matter that suppress single scattering events for a finite range of wavenumbers around the origin in reciprocal space. We derive analytical formulas for the nearest-neighbor functions of disordered stealthy systems. First, we analyze asymptotic small-$r$ approximations and bounding expressions of the nearest-neighbor functions based on the pseudo-hard-sphere ansatz. We then determine how many of the standard $n$-point correlation functions are needed to determine the nearest neighbor functions, and find that a finite number suffice. Via theoretical and computational methods, we compare the large-$r$ behavior of these functions for disordered stealthy systems to those belonging to crystalline lattices. Such ordered and disordered stealthy systems have bounded hole sizes. However, we find that the approach to the critical-hole size can be quantitatively different. We argue that the probability of finding a hole close to the critical-hole size should decrease as a power law with an exponent only dependent on the space dimension $d$ for ordered systems, but that this probability decays asymptotically faster for disordered systems. This implies that holes close to the critical-hole size are rarer in disordered systems. The rarity of observing large holes in disordered systems creates substantial numerical difficulties in sampling the nearest neighbor distributions near the critical-hole size. This motivates both the need for new computational methods for efficient sampling and the development of novel theoretical methods. We also devise a simple analytical formula that accurately describes these systems in the underconstrained regime for all $r$. These results provide a foundation for the analytical description of the nearest-neighbor functions of stealthy systems in the disordered, underconstrained regime.
