对Morse和Charbonneau关于“$d=2$和$d=3$中随机密堆积的显式解析解“一文的答复
Reply to Morse and Charbonneau on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"
摘要：
Morse和Charbonneau的评论表明，我们最近的随机密堆积（RCP）问题的解析解与$d<6$维的堆积数据吻合得很好，但偏离了$d\geq6$维的数据。在这篇回复中，我们认为，使用的结果有关的$E_{8}$李群，没有RCP解决方案的基础上接触数和边际稳定性，预计捕捉RCP在大空间维度$d \geq 8$，其中一个大的差距之间存在的最近的邻居已经在$d=8$。事实仍然是[A]中的结果。Zaccone，Phys. Rev. Lett. 128，028002（2022）]是目前唯一基于统计参数的RCP问题的简单分析解决方案，它捕获了$d=2,3,4,5$中大量的底层物理。
英文摘要：
A Comment by Morse and Charbonneau shows that our recent analytical solution to the random close packing (RCP) problem is in good agreement with packings data in dimensions $d<6$ but deviates from the data for $d\geq6$. In this Reply we argue, using results related to the $E_{8}$ Lie group, that no RCP solution based on contact numbers and marginal stability is expected to capture RCP in large space dimensions $d \geq 8$ where a large gap exists between nearest neighbours already at $d=8$. The fact remains that the result in [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is currently the only simple analytical solution to the RCP problem based on statistical arguments, which captures a good deal of the underlying physics in $d=2,3,4,5$.
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