Hyperuniform states of matter

Abstract

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of longwavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties.

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

“…Disordered hyperuniform many-particle systems are exotic amorphous states of matter that are like crystals in the manner in which their large-scale density fluctuations are anomalously suppressed and yet behave like typical liquids or glasses in that they are statistically isotropic without any Bragg peaks. More precisely, hyperuniform point configurations possess a structure factor S(k) that goes to zero as the wavenumber |k| vanishes [17,18], i.e., lim |k|→0 S(k) = 0.…”

“…For a large class of ordered and disordered systems, the number variance σ 2 (R) has the following large-R asymptotic behavior [17,18]:…”

“…On the other hand, when A > 0 and B = 0, the system is hyposurficial ; examples include homogeneous Poisson point patterns and hypothetical hardsphere systems [17]. Finally, in anti-hyperuniform systems lim |k|→0 S(k) = +∞ (9) and A becomes unbounded [18]. Anti-hyperuniform systems include fractals as well as systems at thermal critical points.…”

“…where α > 0, hyperuniform systems can be categorized into three different classes according to the large-R asymptotic scaling of the number variance [18]:…”

On‐Chip Hyperuniform Lasers for Controllable Transitions in Disordered Systems

“…Hyperuniformity is a disordered phase of matter that enables a large variety of phenomena and applications including free form waveguides and resonators, induced transparency, enhanced Raman spectroscopy, and wavefront engineering via flat optics . While the majority of current studies focus on linear properties of hyperuniform structures, effects arising from nonlinear effects are less known.…”