论文标题
堵塞堆积状态的振动密度：平均场理论
Vibrational density of states of jammed packing: mean-field theory
论文作者
论文摘要
几种平均场理论预测，可以通过在大空间尺寸的极限$ d \ to \ infty $的限制中使用随机矩阵来编写无定形固体的Hessian矩阵。在这些结果的动机上，我们在这里提出了一种将无定形固体的黑森映射到随机矩阵的方法。通过确定随机矩阵的系数，可以使随机矩阵的痕迹与原始系统的Hessian重合。我们将我们的结果与以前在几个空间尺寸的谐波球的数值模拟$ d = 3 $，$ 5 $和$ 9 $进行了比较。对于小压力$ p \ ll 1 $（靠近干扰），即使在$ d = 3 $中，我们也找到了一个良好的协议，并在较大的$ d $中获得更好的协议，这表明近似确实在大空间维度的极限中变得精确。
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a Hessian of the amorphous solid to a random matrix. This is possible by determining the coefficients of a random matrix so that the trace of the random matrix coincides with the Hessian of the original system. We compare our result with that of previous numerical simulations of harmonic spheres in several spatial dimensions $d=3$, $5$, and $9$. For small pressure $p\ll 1$ (near jamming), we find a good agreement even in $d=3$, and obtain better agreements in larger $d$, suggesting that the approximation indeed becomes exact in the limit of large spatial dimensions.
