Universal Hyperuniformity in Active Field Theories

TL;DR

This paper demonstrates that a broad class of active field theories exhibit universal hyperuniformity, showing suppressed long-range density fluctuations similar to passive systems, with activity influencing higher-order correlations.

Contribution

It establishes the universality of hyperuniformity in active scalar field theories and highlights activity-dependent higher-order correlations beyond two-point measures.

Findings

Active field theories are universally hyperuniform.

Density fluctuations resemble passive hyperuniform fields.

Higher moments reveal activity-dependent correlations.

Abstract

We show that dry scalar-order active field theories (AFTs) are universally hyperuniform, i.e., density fluctuations are anomalously suppressed in the long-time limit regardless of the integrability or functional form of the active contributions up to third order in gradient terms. These AFTs include Active model B, Active model B+, and effective Cahn-Hilliard models. Moreover, density variances and spectral densities are virtually indistinguishable from that of passive phase-separated hyperuniform fields. Higher moments of the density fluctuations, however, reveal activity-dependent higher-order correlations that are not captured by conventional two-point measures that characterize hyperuniformity.