We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as ${\omega }^3$ at low frequencies $\omega$, and a contribution to the distribution of energy barriers $\mathrm{\Delta }H$ that scales as $\mathrm{\Delta }{H}^{-1/3}$ at low barrier heights.

中文翻译：

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载荷作用下无摩擦球的堆积填料的不稳定性

我们考虑了由球的拥挤堆积模拟的玻璃对振动态密度的影响以及初期不稳定性的能垒高度的分布。接近不稳定状态时，正常模式的频率和能垒进入新的基态的高度都会消失。这些不稳定性对振动状态的密度做出了贡献，振动状态的密度随着${\omega }^3$ 在低频下 $\omega$，并为能垒的分布做出了贡献 $\mathrm{\Delta }H$ 缩放为 $\mathrm{\Delta }{H}^{-\mathrm{1个}/3}$ 在较低的障碍物高度。