Ensemble Theory for Stealthy Hyperuniform Disordered Ground States

Abstract

It has been shown numerically that systems of particles interacting with "stealthy" bounded, long-ranged pair potentials (similar to Friedel oscillations) have classical ground states that are, counterintuitively, disordered, hyperuniform and highly degenerate. Disordered hyperuniform systems have been receiving recent attention because they are distinguishable exotic states of matter poised between a crystal and liquid with novel properties. The task of formulating an ensemble theory that yields analytical predictions for the structural characteristics and other properties of stealthy degenerate ground states in $d$-dimensional Euclidean space is highly nontrivial because the dimensionality of the configuration space depends on the number density $\rho$ and there is a multitude of ways of sampling the ground-state manifold, each with its own probability measure. The purpose of this paper is to take some initial steps in this direction. Specifically, we derive general exact relations for thermodynamic properties that apply to any ground-state ensemble as a function of $\rho$ in any $d$, and show how disordered degenerate ground states arise as part of the ground-state manifold. We then specialize our results to the canonical ensemble by exploiting an ansatz that stealthy states behave remarkably like "pseudo" equilibrium hard-sphere systems in Fourier space. Our theoretical predictions for the structure and thermodynamic properties of the stealthy disordered ground states and associated excited states are in excellent agreement with computer simulations across the first three space dimensions. The development of this theory provides provide new insights regarding our fundamental understanding of the nature and formation of low-temperature states of amorphous matter. Our work also offers challenges to experimentalists to synthesize stealthy ground states at the molecular level.

22 pages, 14 figures, 5 tables

References in corpus (12)

• Designer disordered materials with large complete photonic band gaps
• Hyperuniformity of critical absorbing states
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Suppressed compressibility at large scale in jammed packings of size disperse spheres
• Collective Coordinate Control of Density Distributions
• Crystalline ground states for classical particles
• Local density of states and Friedel oscillation in graphene
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Gaussian core model phase diagram and pair correlations in high Euclidean dimensions