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Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
Physical Review E ( IF 2.4 ) Pub Date : 2020-03-17 , DOI: 10.1103/physreve.101.032124
Ge Zhang , Salvatore Torquato

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function g2(r) or its corresponding structure factor S(k) is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including d-dimensional Gaussian structure factors, d-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the d-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. Our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for g2(r) and S(k) associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

中文翻译:

通过有效的对相互作用实现具有目标光谱功能的可实现的超均匀和非超均匀粒子配置

识别与对相关函数的目标功能形式相关的可实现多体配置的能力 G2[R 或其相应的结构因子 小号ķ具有重大的基础和现实意义。尽管有明显的必要条件,但规定的结构因子在数密度下ρ为了满足配置上的可实现性,由于具有不同的高阶相关函数的配置的无限简并性,通常不知道足够的条件。本文的主要目的是扩展我们对对相关函数或结构因子类别的理论知识,该对相关函数或结构因子可通过经典的无序粒子结构集成体实现,包括奇异的“超均匀”变体。我们首先介绍一种理论形式主义,该理论形式提供了从具有某些成对加性势的正则合奏中绘制经典粒子构型的方法,这些势能可能对应于结构因子的目标分析功能形式。这种表述使我们能够设计出一种改进的算法,只要有可能,就可以使用这种目标对统计信息来系统地构建规范的整体粒子配置。作为概念的证明,我们通过跨已知可实现的维度上的几个不同结构因子和一个已知不可实现的超统一目标来测试算法。我们的算法对所有可实现的目标都成功,而对无法实现的目标则适当地失败,这证明了该方法对可实现性问题进行数值研究的准确性和功效。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 只要可实现。作为概念的证明,我们通过跨已知可实现的维度上的几个不同结构因子和一个已知不可实现的超统一目标来测试算法。我们的算法对所有可实现的目标都成功,而对无法实现的目标则适当地失败,这证明了该方法对可实现性问题进行数值研究的准确性和功效。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 只要可实现。作为概念的证明,我们通过跨已知可实现的维度上的几个不同结构因子和一个已知不可实现的超统一目标来测试算法。我们的算法对所有可实现的目标都成功,而对无法实现的目标则适当地失败,这证明了该方法对可实现性问题进行数值研究的准确性和功效。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 我们通过针对已知可实现的维度上的几个不同结构因子和已知不可实现的一个超均匀目标来测试算法。我们的算法对所有可实现的目标都成功,而对无法实现的目标则适当地失败,这证明了该方法对可实现性问题进行数值研究的准确性和功效。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 我们通过跨已知可实现的维度上的几个不同结构因子和一个已知不可实现的超统一目标来测试算法。我们的算法对所有可实现的目标都成功,而对无法实现的目标则适当地失败,这证明了该方法对可实现性问题进行数值研究的准确性和功效。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 证明了该方法进行数值研究的准确性和有效性。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括 证明了该方法进行数值研究的准确性和有效性。随后,我们还针对满足已知必要可实现性条件但未知通过无序超均匀点配置可实现的几个结构因子函数族,包括d维高斯结构因子, d一维等离子体二维(OCP)的三维概括,以及 d先前OCP案例的三维傅立叶对偶。此外,我们还探索了不寻常的非匀称目标,包括“超曲线”和“反超匀称”的例子。在所有这些情况下,都可以高精度地实现目标结构因子,这表明它们确实可以通过在正温度下具有成对相互作用的平衡构型实现。值得注意的是,我们还表明,由两体,三体和四体相互作用指定的非平衡完美玻璃的结构因子,也可以通过在正温度下的平衡对相互作用来实现。我们的发现使我们推测,与平移不变的平衡系统或非平衡系统相对应的任何可实现的结构因子都可以通过仅涉及有效对相互作用的平衡集成来实现。G2[R小号ķ与跨维度的无序点配置有关,但也加深了我们对多体物理的理解。而且,我们的工作可以应用于具有理想物理特性的材料的设计,这些材料可以通过其配对统计进行调整。
更新日期:2020-03-19
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