Related papers: Hyperuniformity of Weighted Particle Systems
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…
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.…
Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales.…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…
We introduce the concept of a hyperuniformity disorder length that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of…
We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity…
Hyperuniform systems are distinguished by an unusually strong suppression of large-scale density fluctuations and, consequently, display a high degree of uniformity at the largest length scales. In some cases, however, enhanced uniformity…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
Extending hyperuniformity from classical to quantum fluctuations in electron systems yields a framework that identifies quantum phase transitions and reveals underlying gap structures through the quantum weight. We study long-wavelength…
Hyperuniformity characterizes a state of matter for which density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an experimental system is hyperuniform is experimentally…
A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…
Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity…
In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…
Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought…