Enhanced hyperuniformity from random reorganization

Daniel Hexner, Paul M. Chaikin, Dov Levine

    Research output: Contribution to journalArticlepeer-review


    Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume v = ℓd scales as σ2ρ ≡ 〈ρ2(ℓ)〉 - 〈ρ〉2 ∼ ℓ-d. Systems whose fluctuations decay faster, σ2ρ ∼ ℓ with d < λ ≤ d + 1, are called hyperuniform. The larger λ, the more uniform, with systems like crystals achieving the maximum value: λ = d + 1. Although finite temperature equilibrium dynamics will not yield hyperuniform states, driven, nonequilibrium dynamics may. Such is the case, for example, in a simple model where overlapping particles are each given a small random displacement. Above a critical particle density ρc, the system evolves forever, never finding a configuration where no particles overlap. Below ρc, however, it eventually finds such a state, and stops evolving. This "absorbing state" is hyperuniform up to a length scale ξ, which diverges at ρc. An important question is whether hyperuniformity survives noise and thermal fluctuations. We find that hyperuniformity of the absorbing state is not only robust against noise, diffusion, or activity, but that such perturbations reduce fluctuations toward their limiting behavior, λ → d + 1, a uniformity similar to random close packing and early universe fluctuations, but with arbitrary controllable density.

    Original languageEnglish (US)
    Pages (from-to)4294-4299
    Number of pages6
    JournalProceedings of the National Academy of Sciences of the United States of America
    Issue number17
    StatePublished - Apr 25 2017


    • Absorbing states
    • Hyperuniformity
    • Manna model
    • Random organization

    ASJC Scopus subject areas

    • General


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