Nearest-neighbor functions for disordered stealthy hyperuniform many-particle systems
Nearest-neighbor functions for disordered stealthy hyperuniform many-particle systems
复制标题
DOI：
10.1088/1742-5468/abb8cb
复制
发表时间：
2020-08
期刊：
影响因子：
--
通讯作者：
T. M. Middlemas;S. Torquato
中科院分区：
文献类型：
--
作者：
T. M. Middlemas;S. Torquato
d维欧几里得空间Rd中的无序隐身多粒子系统是物质的奇异无定形状态，它抑制了在互易空间中围绕原点的有限波数范围内的任何单一散射事件。它们是目前引起强烈的基础和实际兴趣的主题。导出了无序隐身多粒子系统最近邻函数的解析公式。首先，我们分析了基于伪硬球分析的最近邻函数的渐近小r逼近和展开式。然后，我们考虑确定需要多少个标准n点相关函数来确定最近邻函数的问题，并发现一个有限的数量就足够了。通过理论和计算方法，我们能够将这些函数在无序隐身系统中的大r行为与那些属于晶体晶格的函数进行比较。这种有序和无序的隐身系统具有有限的孔尺寸，因此对其最近邻函数的支持是紧凑的。然而，我们发现临界孔尺寸的方法可以在数量上不同，强调孔统计在区分有序和无序隐身构型中的重要性。我们认为，对于有序系统，找到接近临界空穴大小的空穴的概率应该以指数仅依赖于空间维数d的幂律的形式减小，但对于无序系统，这种概率衰减得渐近更快，要么幂律的指数增加，要么进入比任何幂律更快的衰减的交叉。这意味着在无序系统中，接近临界孔尺寸的孔很少。在无序系统中很少观察到大孔，这给在临界孔尺寸附近采样最近邻分布带来了实质性的数值困难。这激发了对有效采样的新计算方法的需求，以及确定接近临界孔尺寸的孔的行为的新理论方法的发展。我们还设计了一个简单的解析公式，可以准确地描述所有r在欠约束状态下的这些系统。这些结果为无序，欠约束状态下隐身系统的最近邻函数的分析描述提供了理论基础，并且可以作为这些系统的材料和输运性质的分析理论的基础。
Disordered stealthy many-particle systems in d-dimensional Euclidean space Rd are exotic amorphous states of matter that suppress any single scattering events for a finite range of wavenumbers around the origin in reciprocal space. They are currently the subject of intense fundamental and practical interest. We derive analytical formulas for the nearest-neighbor functions of disordered stealthy many-particle systems. First, we analyze asymptotic small-r approximations and expansions of the nearest-neighbor functions based on the pseudo-hard-sphere ansatz. We then consider the problem of determining 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 are able to 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, and thus compact support for their nearest-neighbor functions. However, we find that the approach to the critical-hole size can be quantitatively different, emphasizing the importance of hole statistics in distinguishing ordered and disordered stealthy configurations. 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, with either an increase in the exponent of the power law or a crossover into a decay faster than any power law. 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 for ascertaining the behavior of holes close to the critical-hole size. We also devise a simple analytical formula that accurately describes these systems in the underconstrained regime for all r. These results provide a theoretical foundation for the analytical description of the nearest-neighbor functions of stealthy systems in the disordered, underconstrained regime, and can serve as a basis for analytical theories of material and transport properties of these systems.