It has been shown that a correlated Wishart ensemble can be used to study the general vibrational properties of stable amorphous solids, where the energy is translationally invariant. The vibrational density of states and the dynamic structure factor of the system have been determined using the random matrix theory. The results indicate the existence of the Ioffe–Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The presented vibrational density of states demonstrates the boson peak at the frequency close to the Ioffe—Regel crossover.

中文翻译：

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基于随机相关矩阵理论的无序系统的普遍振动性质

研究表明，相关的Wishart系综可用于研究能量稳定地不变的稳定无定形固体的一般振动性质。使用随机矩阵理论已经确定了系统的状态振动密度和动态结构因子。结果表明，低频传播声子与高频扩散子之间存在艾菲-雷格尔分频。所呈现的状态振动密度表明，玻色子峰的频率接近Ioffe-Regel交叉。