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arXiv 2103.14989cond-mat.softcond-mat.mtrl-scicond-mat.stat-mech
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多粒子系统接近超一致态的结构特征

Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States

Salvatore Torquato

摘要:

我们探索的定量描述符,预示着当一个多粒子系统在$d$维欧几里德空间$\mathbb{R}^d$接近超均匀状态的相关控制参数的函数。我们建立了定量的标准,以确定超均匀和非超均匀的距离标度制度n的比例$B/A$,其中$A$是“体积”系数和$B$是“表面积”系数与局部数方差$σ^2(R)$半径$R$的球形窗口的程度。为了补充已知的直接空间表示的系数$B$的总相关函数$h({\bf r})$,我们推导出其相应的傅立叶表示的结构因子$S({\bf k})$,这是特别有用的散射信息时,实验或理论上。我们表明,自由体积理论的压力的平衡包装相同的硬球,接近一个严格堵塞的状态,无论是沿着稳定的晶体或亚稳态无序分支规定,这样的最终状态是完全超均匀的。利用比值$B/A$、超均匀性指数$H$和直接相关函数长度尺度$ξ_c$,我们研究了三个不同的精确可解模型作为相关控制参数的函数,无论是密度还是温度,其端态都是完全超均匀的。我们分析了平衡硬棒和“粘性”硬球系统在任意空间维度$d$作为密度的函数。我们还研究了低温激发态的多粒子系统相互作用的“隐形”长程对相互作用的温度趋于零。识别超均匀标度制度的能力在分析实验或计算生成的样本中应该特别有用,这些样本必须是有限大小的。

英文摘要:

We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes n terms of the ratio $B/A$, where $A$ is "volume" coefficient and $B$ is "surface-area" coefficient associated with the local number variance $σ^2(R)$ for a spherical window of radius $R$. To complement the known direct-space representation of the coefficient $B$ in terms of the total correlation function $h({\bf r})$, we derive its corresponding Fourier representation in terms of the structure factor $S({\bf k})$, which is especially useful when scattering information is available experimentally or theoretically. We show that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio $B/A$, the hyperuniformity index $H$ and the direct-correlation function length scale $ξ_c$, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. We analyze equilibrium hard rods and "sticky" hard-sphere systems in arbitrary space dimension $d$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "stealthy" long-ranged pair interactions as the temperature tends to zero. The capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally- or computationally-generated samples that are necessarily of finite size.

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