Hyperuniformity and its Generalizations

Abstract

Disordered many-particle hyperuniform systems are exotic amorphous states characterized by anomalous suppression of large-scale density fluctuations. Here we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, as well as statistically anisotropic many-particle systems and two-phase media. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems , physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of divergence-free random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. We show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical and acoustic characteristics) to these states of matter. Such tunablity could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity.

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Cited by in corpus (10)

• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Hyperuniformity of Quasicrystals
• Random Scalar Fields and Hyperuniformity
• Disordered Hyperuniform Heterogeneous Materials
• Stealth acoustic materials
• Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations
• Classical many-particle systems with unique disordered ground states
• Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance
• Equidistribution of jellium energy for Coulomb and Riesz Interactions