论文标题
带有随机矩阵的颗粒包装的振动光谱
Vibrational Spectrum of Granular Packings With Random Matrices
论文作者
论文摘要
颗粒包装的振动光谱可以用作干扰过渡的标志，零频率的状态密度在过渡时变为非零。以前已经提出，颗粒堆的振动光谱可以大约从随机矩阵理论中获得。在这里我们表明，尽管随机矩阵理论预测的状态密度与动态数值模拟的某些方面不一致，但状态密度的相关性（与状态的密度相反，与状态的密度相反 - 预计将是普遍的 - 确实表现出良好的一致性在串联的动态数值模拟和分析量的lagogogogyerre lagogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogogeerre sense中均具有良好的一致性。同时，高斯正交合奏明显分歧。这些发现表明，Laguerre合奏正确地重现了堵塞的颗粒物的通用统计特性，并排除了高斯正交集合。我们还提出了一个随机晶格模型，该模型是随机矩阵集合的物理动机变体。数值计算表明，该模型重现了颗粒状物质状态振动密度的已知特征，同时还保留了Laguerre随机矩阵理论中看到的相关结构。因此，我们建议可以应用随机晶格模型，不仅可以理解频谱，而且可以理解珠子包振动的更一般特性，包括在干扰点和远离它的模式的空间结构。
The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming non-zero at the transition. It has been proposed previously that the vibrational spectrum of granular packings can be approximately obtained from random matrix theory. Here we show that although the density of states predicted by random matrix theory does not agree with certain aspects of dynamical numerical simulations, the correlations of the density of states, which---in contrast to the density of states---are expected to be universal, do show good agreement between dynamical numerical simulations of bead packs near the jamming point and the analytic predictions of the Laguerre orthogonal ensemble of random matrices. At the same time, there is clear disagreement with the Gaussian orthogonal ensemble. These findings establish that the Laguerre ensemble correctly reproduces the universal statistical properties of jammed granular matter and exclude the Gaussian orthogonal ensemble. We also present a random lattice model which is a physically motivated variant of the random matrix ensemble. Numerical calculations reveal that this model reproduces the known features of the vibrational density of states of granular matter, while also retaining the correlation structure seen in the Laguerre random matrix theory. We propose that the random lattice model can therefore be applied the understand not only the spectrum but more general properties of the vibration of bead packs including the spatial structure of modes both at the jamming point and far from it.
