期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2017
卷号：114
期号：17
页码：4294-4299
DOI：10.1073/pnas.1619260114
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume v = ℓ d scales as σ ρ 2 ≡ ⟨ ρ 2 ( ℓ ) ⟩ − ⟨ ρ ⟩ 2 ∼ ℓ − d . Systems whose fluctuations decay faster, σ ρ 2 ∼ ℓ − λ 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 ρ c , the system evolves forever, never finding a configuration where no particles overlap. Below ρ c , however, it eventually finds such a state, and stops evolving. This “absorbing state” is hyperuniform up to a length scale ξ , which diverges at ρ c . 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.
关键词：random organization ; absorbing states ; hyperuniformity ; Manna model
