AI 中文总结
研究发现普通无序材料能支持超均匀物理场，开发通用理论框架，通过局部物理算符从母场生成导出场，利用算符的傅里叶符号特性抑制长波长涨落，拓宽了超均匀性概念。
AI 中文摘要
无序物质中的涨落在决定材料性质和物理响应方面起着核心作用。近期研究发现了一类特殊的结构超均匀材料，其通过粒子、相或微观结构特征的特殊空间组织异常抑制了大规模密度涨落。本文证明普通的、结构上非超均匀的无序材料仍能支持超均匀的物理标量、矢量和张量场，如电荷、束缚电流、涡度、缺陷密度和应力。我们开发了一个通用理论框架，通过局部物理算符从更原始的母场生成物理场。在傅里叶空间中，导出场的频谱由母场频谱和算符的傅里叶符号的乘积决定。当算符体现局部规范类约束时，其傅里叶符号在小波数处有零点，消除了相应的长波长涨落。结果，导出场表现出对无限波长强度涨落的完全抑制，无论母场的大规模无序和非超均匀性如何。我们在弹性、静电和静磁环境中证明了这一机制，表明即使其母本征应变、极化或磁化场保持传统的无序状态，算符生成的不相容性、束缚电荷和束缚电流场也能变得超均匀。这些发现将超均匀性的概念从物质的结构性质扩展到由局部物理约束产生的普遍场现象。
英文摘要
Fluctuations in disordered matter play a central role in determining material properties and physical responses. Recent studies have identified an exotic class of systems known as structurally hyperuniform materials, in which large-scale density fluctuations are anomalously suppressed through special spatial organization of particles, phases, or microstructural features. Here we demonstrate that ordinary, structurally nonhyperuniform disordered materials can nevertheless support hyperuniform physical scalar, vector, and tensor fields such as charge, bound current, vorticity, defect density, and stress. We develop a general theoretical framework in which a physical field is generated from a more primitive parent field through a local physical operator. In Fourier space, the spectrum of the derived field is determined by the product of the parent-field spectrum and the Fourier symbol of the operator. When the operator embodies a local gauge-like constraint, its Fourier symbol possesses zeros at small wavenumber, eliminating the corresponding long-wavelength fluctuations. As a consequence, the derived field exhibits complete suppression of infinite-wavelength intensity fluctuations, irrespective of the large-scale disorder and nonhyperuniformity of the parent field. We demonstrate this mechanism in elastic, electrostatic, and magnetostatic settings, showing that operator-generated incompatibility, bound charge, and bound-current fields can become hyperuniform even when their parent eigenstrain, polarization, or magnetization fields remain conventionally disordered. These findings broaden the notion of hyperuniformity from a structural property of matter to a universal field phenomenon generated by local physical constraints.
