Hyperuniformity information

Hyperuniform materials are characterized by an anomalous suppression of density fluctuations at large scales. More precisely, the vanishing of density fluctuations in the long-wave length limit (like for crystals) distinguishes hyperuniform systems from typical gases, liquids, or amorphous solids.^[1][2] Examples of hyperuniformity include all perfect crystals,^[1] perfect quasicrystals,^[3][4] and exotic amorphous states of matter.^[2]

Quantitatively, a many-particle system is said to be hyperuniform if the variance of the number of points within a spherical observation window grows more slowly than the volume of the observation window. This definition is equivalent to a vanishing of the structure factor in the long-wavelength limit,^[1] and it has been extended to include heterogeneous materials as well as scalar, vector, and tensor fields.^[5] Disordered hyperuniform systems, were shown to be poised at an "inverted" critical point.^[1] They can be obtained via equilibrium or nonequilibrium routes, and are found in both classical physical and quantum-mechanical systems.^[1][2] Hence, the concept of hyperuniformity now connects a broad range of topics in physics,^{[2][6][7][8][9]} mathematics,^{[10][11][12][13][14][15]} biology,^[16][17][18] and materials science.^[19][20][21]

The concept of hyperuniformity generalizes the traditional notion of long-range order and thus defines an exotic state of matter. A disordered hyperuniform many-particle system can be statistically isotropic like a liquid, with no Bragg peaks and no conventional type of long-range order. Nevertheless, at large scales, hyperuniform systems resemble crystals, in their suppression of large-scale density fluctuations. This unique combination is known to endow disordered hyperuniform materials with novel physical properties that are, e.g., both nearly optimal and direction independent (in contrast to those of crystals that are anisotropic).^[2]