周期性与超均匀性的准正规模式特征

中文摘要 AI 辅助

超均匀材料处于周期性有序与常规无序之间的中间状态，其特征是长波长密度波动受到抑制，通常通过结构因子来量化。然而，这种表征依赖于扩展构型或超胞表示的统计特性，无法直接描述有限结构的共振响应，而有限结构是散射实验中常见的对象。本文引入准正规模式谱作为补充框架，用于表征有限隐形超均匀材料的波动特性。我们分析了在不同隐形参数（χ）下周期性结构和隐形超均匀结构的复本征频率，研究了散射体的空间组织如何编码在准正规模式的频率和空间分布中。我们发现，随着超均匀度的变化，准正规模式谱会发生系统性变化，揭示了仅靠结构因子无法捕捉的特征。特别是，共振态的演化为有限系统的结构关联与散射响应之间建立了直接联系。我们的研究结果确立了准正规模式作为超均匀性的实空间和开放系统表征，并为从散射和共振动力学角度比较离散异质材料提供了统一框架。

英文摘要

Hyperuniform materials occupy an intermediate regime between periodic order and conventional disorder, characterized by a suppression of long-wavelength density fluctuations, commonly quantified by the structure factor. This characterization, however, relies on the statistical properties of an extended configuration or supercell representation and does not directly describe the resonant response of a finite structure, as typically encountered in scattering experiments. Here, we introduce the quasi-normal-mode spectrum as a complementary framework for characterizing the wave properties of finite stealthy hyperuniform materials. We analyze the complex eigenfrequencies of both periodic and stealthy hyperuniform structures over a range of the stealthiness parameter ($χ$), and investigate how the spatial organization of scatterers is encoded in both frequency and spatial profiles of their quasi-normal modes. We find systematic changes in the quasi-normal modes spectrum as the degree of hyperuniformity is varied, revealing signatures that are not captured solely by the structure factor. In particular, the evolution of the resonant states provides a direct connection between structural correlations and the scattering response of finite systems. Our results establish quasi-normal modes as a real-space and open-system characterization of hyperuniformity and provide a unified framework for comparing discrete heterogeneous materials from the perspective of their scattering and resonant dynamics.

发表机构

• Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València（瓦伦西亚理工大学纯数学和应用数学大学研究所）

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