通过有效对相互作用实现具有目标谱函数的超均匀和非超均匀粒子组态
Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
摘要：
识别与对关联函数$g_2(r)$或其相应的结构因子$S(k)$的目标函数形式相关的可实现的多体构型的能力具有重要的基础和实际意义。本文的一个主要目的是扩大我们的理论知识的类对关联函数或结构因子，是由经典的粒子配置无序合奏实现。我们首先介绍了一种理论形式主义，提供了一种方法来绘制经典的粒子配置从典型的合奏与一定的成对添加剂的潜力，可以对应于有针对性的分析功能形式的结构因子。这种提法使我们能够设计一种改进的算法来系统地构建正则系综粒子配置与这样的目标对统计。我们测试的算法，针对几个不同的结构因素，已知是可实现的，一个超均匀的目标，是已知的nontrivially不可实现的尺寸。随后，我们还针对几个家庭的结构因子函数，满足已知的必要的可实现性条件，但迄今为止还不知道是可实现的。此外，我们还探讨了不寻常的非超均匀目标，包括“hyposurgery”和“反超均匀”的例子。在所有这些情况下，目标结构因子都以高精度实现，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来实现。我们的研究结果使我们的猜想，任何可实现的结构因子对应于一个平衡不变的平衡或非平衡系统可以通过一个平衡系综只涉及有效的对相互作用。
英文摘要：
The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2(r)$ or its corresponding structure factor $S(k)$ is of great fundamental and practical importance. 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. 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. 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. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but were heretofore not known to be realizable. Moreover, we also explore unusual nonhyperuniform targets, including "hyposurficial" and "anti-hyperuniform" examples. In all of these instances, the targeted structure factors were achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise 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.
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