无序超均匀调制相与来自单一自由能的宇宙网

中文摘要 AI 辅助

无序超均匀性跨越二十五个数量级，从软物质和凝聚态物质的微观世界到宇宙中物质的分布。我们引入了一个无可调耦合的自由能泛函，包含一个相场晶体有序项和一个牛顿尾项，并证明其两个动力学极限生成了这两种结构。在守恒过阻尼动力学下，它停滞在一种双连续迷宫结构中，这种结构见于受限流体、嵌段共聚物、活性物质和植被图案中，属于第三类无序超均匀态；在膨胀背景下的惯性动力学中，它生成一个宇宙网，其潮汐骨架在每一形态类别中与仅由引力产生的骨架相差在0.03以内。在两种极限中，被抑制的长波长涨落继承自初始条件而非由动力学产生：停滞态的大尺度指数等于原初指数，而引力将红外谱按线性增长因子重新标度，在1363倍增长范围内误差优于百分之一。这两个扇区连续相连，且其距离可测量：一旦有序调制饱和，其平均场反作用使介质留下一个正比于λ0^2的残余压力，该压力通过一个平滑因子抑制最大尺度的增长，并在冷物质极限λ0→0时消失。

英文摘要

Disordered hyperuniformity spans twenty-five orders of magnitude, from the microscopic world of soft and condensed matter to the distribution of matter in the universe. We introduce a free-energy functional with no adjustable coupling, a phase-field-crystal ordering term and a Newtonian tail, and show that its two kinetic limits generate two of these structures. Under conserved overdamped dynamics it arrests in a bicontinuous labyrinth of the kind found in confined fluids, block copolymers, active matter and vegetation patterns, which is a class III disordered hyperuniform state; under inertial dynamics in an expanding background it generates a cosmic web whose tidal skeleton matches that of gravity alone to within $0.03$ in every morphological class. In both limits the suppressed long-wavelength fluctuations are inherited from the initial condition rather than made by the dynamics: the large-scale exponent of the arrested state equals the primordial one, and gravity rescales the infrared spectrum by the linear growth factor to better than one per cent over a factor $1363$ of growth. The two sectors are continuously connected, and their distance is measurable: once the ordering modulation saturates, its mean-field back-reaction leaves the medium with a residual pressure proportional to $λ_0^2$ that suppresses the growth of the largest scales by a smooth factor and vanishes in the cold-matter limit $λ_0\to0$.

发表机构

• CNR-Istituto dei Sistemi Complessi（意大利国家研究委员会复杂系统研究所）
• Dipartimento di Fisica, Universitá La Sapienza di Roma（罗马大学物理系）

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