Vibrational density of states of jammed packing at high dimensions: Mean-field theory
Vibrational density of states of jammed packing at high dimensions: Mean-field theory
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高维堵塞堆积状态的振动密度：平均场理论
DOI：
10.1103/physreve.106.024904
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发表时间：
2022
影响因子：
2.4
通讯作者：
Shimada Masanari
中科院分区：
文献类型：
--
作者：
Ikeda Harukuni;Shimada Masanari
几种平均场理论预测，非晶态固体的海森矩阵在大空间维度的极限内收敛于Wishart矩阵。在这些结果的启发下，我们通过将原始系统的黑森映射到Wishart矩阵，计算了调和球体随机堆积的态密度。我们将我们的结果与以前对调和球体在5维和9维空间中的数值模拟结果进行了比较。对于小气压(近干扰)，我们发现即使在小气压下也是很好的一致，而在更大的维上我们也得到了更好的一致，这表明该近似在极限上是精确的。
Several mean-field theories predict that the Hessian matrix of amorphous solids converges the Wishart matrix in the limit of the large spatial dimensions. Motivated by these results, we calculate here the density of states of random packing of harmonic spheres by mapping the Hessian of the original system to the Wishart matrix. We compare our result with that of previous numerical simulations of harmonic spheres in several spatial dimensions, 5, and 9. For small pressure(near jamming), we find a good agreement even in, and obtain better agreements in larger, suggesting that the approximation becomes exact in the limit.