The two-dimensional one-component plasma is hyperuniform

TL;DR

This paper proves that the two-dimensional one-component plasma exhibits hyperuniformity at all positive temperatures, meaning particle number fluctuations grow slower than the area of large regions, indicating suppressed density fluctuations.

Contribution

The authors establish the hyperuniformity of the 2D one-component plasma at all positive temperatures, a significant theoretical result in Coulomb systems.

Findings

Variance of particle number grows slower than area in large disks

System exhibits hyperuniformity at all positive temperatures

Provides rigorous proof for hyperuniformity in Coulomb gases

Abstract

We prove that at all positive temperatures in the bulk of a classical two-dimensional one-component plasma (also called Coulomb or log-gas, or jellium) the variance of the number of particles in large disks grows (strictly) more slowly than the area. In other words the system is hyperuniform.