论文标题
通过有效的配对相互作用，具有靶向光谱函数的可实现的超明均匀和非液相均匀粒子构型
Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
论文作者
论文摘要
识别与针对对相关功能的目标功能形式相关的可实现多体配置的能力$ g_2（r）$或其相应的结构因子$ s（k）$具有很大的基本和实际重要性。本文的主要目的是扩展我们对通过粒子构型的经典无序集合可以实现的对相关函数类别或结构因子类别的理论知识。我们首先引入了一种理论形式主义，该形式提供了一种手段，可以从具有某些成对添加电位的规范合奏中绘制经典的粒子构型，这些势能可能与结构因子的有针对性的分析功能形式相对应。这种公式使我们能够设计一种改进的算法，以使用此类目标对统计构建系统的规范 - 构造粒子构型。我们通过靶向跨维数的几个不同结构因子来测试算法，这些算法已知是可实现的，而一个非常均匀的靶标在不可忽视的情况下是不可通行的。随后，我们还针对几个符合已知必要的可实现条件但迄今为止无法实现的结构性因素函数家族。此外，我们还探讨了异常的非液均匀靶标，包括“不透明”和“抗骨均匀”示例。在所有这些情况下，靶向结构因子都是高精度实现的，这表明它们确实可以通过在正温度下成对相互作用的平衡构型来实现。我们的发现使我们提出了这样一个猜想，即任何与不变的平衡或非平衡系统相对应的可实现结构因子都可以通过仅涉及有效的成对相互作用的平衡集合来实现。
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.
