The two-dimensional one-component plasma is hyperuniform

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 more slowly than the area. In other words the system is hyperuniform.We obtain a non-sharp but quantitative bound on the number variance's growth rate, which is the first mathematical justification of an old prediction in the physics literature about "suppression of charge fluctuations".We introduce an argument of approximate conditional independence for well-separated sub-systems and a trick using "isotropically averaged localized translations" in order to control the expectation of non-smooth linear statistics.1 Our argument works for α > 31 32 .

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

“…13,[16][17][18] The property that number uctuations over an observation volume scale with the area is nowadays termed hyperuniformity, and is a generic feature of particle systems with long-range 1/r interactions, where r is the interparticle distance. [60][61][62] We may rationalize this behaviour with sDFT: from eqn (7), static charge uctuations integrate the static structure factor as…”

“…Yet, electrolytes are but a special case of particles with long-range interactions (decaying as 1/r where r is the distance between particles), which include also one-component plasmas, active particles, and many others. [59][60][61][62]96,97 A recent investigation showed remarkable results where long-range correlations were observed both in driven electrolytes and active particle systems, 95,98 for the same underlying mathematical reason. This raises the question of whether the time-dependent behaviour uncovered in the present work extends to this broad class of systems and whether other universal signatures may be unravelled.…”

“…[12][13][14][15][16][17][18] - a generic phenomenon termed hyperuniformity. [58][59][60][61][62] How does this screening behaviour pertain in time? Furthermore, dynamic features of electrolytes, such as conductivity, are not characterized by a universal timescale.…”