Quasi-normal-mode signatures of periodicity and hyperuniformity

Abstract

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.