跨空间维度的超球最大随机密堆积（MRJ）的超均匀性
Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions
AI总结：
研究通过生成d=3、4、5维高质量严格密堆积MRJ构型，确认真正密堆积与超均匀性的关键联系，提出理想MRJ满足α=d−2且随维度更超均匀。
摘要：
最大随机密堆积（MRJ）状态是严格密堆积（力学刚性）且互不重叠物体的最随机构型。MRJ堆积具有超均匀性，这意味着与典型无序系统相比，其长波密度涨落受到异常抑制，即其结构因子$S(\mathbf{k})$随波数$|\mathbf{k}|$趋于零而趋于零。本文表明，在空间维度$d=3、4和5$中生成高质量的严格密堆积状态，对于确保超均匀性并提取MRJ状态的超均匀指数$α>0$的精确值至关重要；该指数由$|\mathbf{k}|\rightarrow0$极限下$S(\mathbf{k})\sim|\mathbf{k}|^α$的幂律行为定义。此外，我们表明，对于固定的$d$，随着粒子数$N$增加，确保密堆积变得更加困难，从而产生非超均匀的堆积。自由体积理论论证表明，理想MRJ状态不包含“rattlers（自由振子）”，后者在数值生成的堆积中充当缺陷。随着$d$增加，我们发现自由振子比例显著下降。我们对最大的真正密堆积堆积的分析表明，所有维度$d\geq3$的理想MRJ堆积都是超均匀的，且$α=d-2$，这意味着堆积随$d$增加而变得更加超均匀。MRJ堆积与近期提出的Manna类随机密堆积（RCP）状态在$α$上的差异——据报道后者在$d=3$时$α=0.25$，并在$d=4$和$d=5$时为非超均匀（$α=0$）——鲜明展示了这些维度中RCP与MRJ状态大尺度结构之间的显著区别。本工作阐明了真正密堆积与超均匀性之间关联的重要性，并推动开发一种生成无自由振子的三维MRJ堆积的算法。
英文摘要：
The maximally random jammed (MRJ) state is the most random configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors $S(\mathbf{k})$ tend to zero as the wavenumber $|\mathbf{k}|$ tends to zero. Here, we show that generating high-quality strictly jammed states for space dimensions $d = 3,4,$ and $5$ is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent $α> 0$ for MRJ states, defined by the power-law behavior of $S(\mathbf{k})\sim|\mathbf{k}|^α$ in the limit $|\mathbf{k}|\rightarrow0$. Moreover, we show that for fixed $d$ it is more difficult to ensure jamming as the particle number $N$ increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As $d$ increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions $d\geq3$ are hyperuniform with $α= d - 2$, implying the packings become more hyperuniform as $d$ increases. The differences in $α$ between MRJ packings and recently proposed Manna-class random close packed (RCP) states, which were reported to have $α= 0.25$ in $d=3$ and be nonhyperuniform ($α= 0$) for $d = 4$ and $d = 5$, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our work clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings.
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