Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states

Abstract

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 faster than the surface area. By targeting a specified form of the structure factor at small wavenumbers using collective density variables, we are able to tailor the form of asymptotic local density fluctuations while simultaneously measuring the effect of imposing weak and strong constraints on the available degrees of freedom within the system. Even in one dimension, the long-range effective interactions induce clustering and nontrivial phase transitions in the resulting ground-state configurations. We provide an analytical connection between the fraction of contrained degrees of freedom within the system and the disorder-order phase transition for a class of target structure factors by examining the realizability of the constrained contribution to the pair correlation function. Our results explicitly demonstrate that disordered hyperuniform many-particle ground states, and therefore also point distributions, with substantial clustering can be constructed. We directly relate the local coordination structure of our point patterns to the distribution of the void space external to the particles, and we provide a scaling argument for the configurational entropy of the systems when only a small fraction of the degrees of freedom are constrained. By emphasizing the intimate connection between geometrical constraints on the particle distribution and structural regularity, our work has direct implications for higher-dimensional systems, including an understanding of the appearance of hyperuniformity and quasi-long-range pair correlations in maximally random strictly jammed packings of hard spheres.

34 pages, 11 figures

References in corpus (15)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Designer disordered materials with large complete photonic band gaps
• Why spin ice obeys the ice rules
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Hyperuniform long-range correlations are a signature of disordered jammed hard-particle packings
• Complete Band Gaps in 2D Photonic Quasicrystals
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Collective Coordinate Control of Density Distributions
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Reformulation of the Covering and Quantizer Problems as Ground States of Interacting Particles
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Realizability of point processes
• New Duality Relations for Classical Ground States
• Tilings of space and superhomogeneous point processes

Cited by in corpus (39)

• Hyperuniform States of Matter
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Hyperuniformity of critical absorbing states
• Hyperuniformity and its Generalizations
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Noise, diffusion, and hyperuniformity
• Hyperuniformity of Quasicrystals
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Stone-Wales Defects Preserve Hyperuniformity in Amorphous Two-Dimensional Materials
• Disordered Hyperuniform Heterogeneous Materials
• The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero
• Improved reconstructions of random media using dilation and erosion processes
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States
• Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices
• Hyperuniformity with no fine tuning in sheared sedimenting suspensions
• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs
• Topological Transformations in Hyperuniform Pentagonal 2D Materials Induced by Stone-Wales Defects
• Classical many-particle systems with unique disordered ground states
• Disordered Hyperuniform Quasi-1D Materials
• 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
• Structural characterization and statistical-mechanical model of epidermal patterns
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• Hyperuniformity Order Metric of Barlow Packings
• Inherent Structures for Soft Long-Range Interactions in Two-Dimensional Many-Particle Systems
• Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
• Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability
• Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials
• Nearest-Neighbor Functions for Disordered Stealthy Hyperuniform Many-Particle Systems
• Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems
• Topological Defects, Inherent Structures, and Hyperuniformity
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions