Hexner Daniel, Chaikin Paul M, Levine Dov
Department Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel.
James Franck Institute, The University of Chicago, Chicago, IL 60637.
Proc Natl Acad Sci U S A. 2017 Apr 25;114(17):4294-4299. doi: 10.1073/pnas.1619260114. Epub 2017 Apr 10.
Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume [Formula: see text] scales as [Formula: see text] Systems whose fluctuations decay faster, [Formula: see text] with [Formula: see text], are called hyperuniform. The larger [Formula: see text], the more uniform, with systems like crystals achieving the maximum value: [Formula: see text] 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 [Formula: see text], the system evolves forever, never finding a configuration where no particles overlap. Below [Formula: see text], however, it eventually finds such a state, and stops evolving. This "absorbing state" is hyperuniform up to a length scale [Formula: see text], which diverges at [Formula: see text] 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, [Formula: see text], a uniformity similar to random close packing and early universe fluctuations, but with arbitrary controllable density.
扩散使密度涨落弛豫至均匀随机状态，其在体积为[公式：见原文]的区域内的方差按[公式：见原文]缩放。涨落衰减更快的系统，即[公式：见原文]且[公式：见原文]，被称为超均匀系统。[公式：见原文]越大，系统越均匀，像晶体这样的系统能达到最大值：[公式：见原文]。尽管有限温度平衡动力学不会产生超均匀状态，但受驱动的非平衡动力学可能会。例如，在一个简单模型中，重叠粒子各自被赋予一个小的随机位移，情况就是如此。在临界粒子密度[公式：见原文]之上，系统会永远演化，永远找不到没有粒子重叠的构型。然而，在[公式：见原文]之下，它最终会找到这样一种状态并停止演化。这个“吸收态”在长度尺度[公式：见原文]内是超均匀的，该长度尺度在[公式：见原文]处发散。一个重要的问题是超均匀性在噪声和热涨落下是否依然存在。我们发现吸收态的超均匀性不仅对噪声、扩散或活性具有鲁棒性，而且这种微扰会使涨落朝着其极限行为[公式：见原文]衰减，这是一种类似于随机密堆积和早期宇宙涨落的均匀性，但密度是任意可控的。
