Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States

Abstract

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 criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes n terms of the ratio $B/A$, where $A$ is "volume" coefficient and $B$ is "surface-area" coefficient associated with the local number variance ${\sigma }^2(R)$ for a spherical window of radius $R$. To complement the known direct-space representation of the coefficient $B$ in terms of the total correlation function $h(\mathbf{r})$, we derive its corresponding Fourier representation in terms of the structure factor $S(\mathbf{k})$, which is especially useful when scattering information is available experimentally or theoretically. We show that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio $B/A$, the hyperuniformity index $H$ and the direct-correlation function length scale ${\xi }_c$, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. We analyze equilibrium hard rods and "sticky" hard-sphere systems in arbitrary space dimension $d$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "stealthy" long-ranged pair interactions as the temperature tends to zero. The capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally- or computationally-generated samples that are necessarily of finite size.

arXiv comment19 pages, 14 figures

References in corpus (40)

• Is Random Close Packing of Spheres Well Defined?
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Mean field theory of hard sphere glasses and jamming
• Designer disordered materials with large complete photonic band gaps
• Hyperuniform States of Matter
• Pair Correlation Function Characteristics of Nearly Jammed Disordered and Ordered Hard-Sphere Packings
• New upper bounds on sphere packings I
• Unexpected Density Fluctuations in Jammed Disordered Sphere Packings
• Hyperuniformity of critical absorbing states
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Stacking Entropy of Hard Sphere Crystals
• Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Hydrodynamics of Random-Organizing Hyperuniform Fluids
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Hyperuniform disordered phononic structures
• Hyperuniformity of Quasicrystals
• Critical slowing down and hyperuniformity on approach to jamming
• Multifunctional Composites for Elastic and Electromagnetic Wave Propagation
• Point processes and stochastic displacement fields
• Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
• The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Large-scale structure and hyperuniformity of amorphous ices
• Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition
• Nonequilibrium static diverging length scales on approaching a prototypical model glassy state
• Voronoi and Voids Statistics for Super-homogeneous Point Processes
• Hidden Multiscale Order in the Primes
• Absorption of scalar waves in correlated disordered media and its maximization using stealth hyperuniformity
• Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions
• Tilings of space and superhomogeneous point processes
• Effect of Window Shape on the Detection of Hyperuniformity via the Local Number Variance
• Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions
• Low-temperature statistical mechanics of the QuanTizer problem: fast quenching and equilibrium cooling of the three-dimensional Voronoi Liquid

Cited by in corpus (20)

• Sub-diffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems
• Local Order Metrics for Two-Phase Media Across Length Scales
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs
• Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions
• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Local order metrics for many-particle systems across length scales
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Realizability of Iso-$g_2$ Processes via Effective Pair Interactions
• Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks
• Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold
• Hyperdisordered cell packing on a growing surface
• Giant density fluctuations in locally hyperuniform states
• Devitrification and Melting Dynamics in Vapor Deposited Water Ice
• Hyperuniformity of Weighted Particle Systems
• Diffusion Spreadability as a Probe of the Microstructure of Complex Media Across Length Scales
• Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media