Hyperuniformity of Weighted Particle Systems

TL;DR

This paper extends the concept of hyperuniformity to weighted particle systems, providing a theoretical framework to analyze large-scale fluctuations in systems with various internal degrees of freedom and attributes.

Contribution

It introduces generalized weighted correlation and spectral functions, revealing that hyperuniformity can change when weights are considered, unlike in unweighted systems.

Findings

Hyperuniformity does not always translate from particles to weights.

Weighted systems can be hyperuniform, antihyperuniform, or nonhyperuniform independently of particle arrangements.

The framework applies to diverse systems like liquids, phases, and ionic liquids.

Abstract

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights: internal degrees of freedom such as scalars, vectors, pseudovectors, directors, tensors, or extrinsic local attributes. Our generalization extends hyperuniformity from fluctuations in particle positions to fluctuations in the spatial distribution of weights. We derive generalized weighted pair correlation, autocovariance, and spectral functions, and show their relation to the local variance in weighted many-particle systems. Applying this formalism to bond-orientational ordered phases, dipolar liquid water, Voronoi-cell volumes, and certain ionic liquids, we demonstrate that hyperuniformity in the particle system does not necessarily translate to hyperuniformity of the weighted system. In fact, cases exist where a hyperuniform particle system becomes antihyperuniform when weighted, and others where nonhyperuniform or antihyperuniform particle systems yield hyperuniform weighted systems. This theoretical framework provides a road map for quantifying large-scale fluctuations in weighted many-particle systems, offering a powerful tool for identifying systems with novel physical properties.