论文标题
无定形固体中玻色子峰和Ioffe-Regel标准的随机矩阵方法
A random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids
论文作者
论文摘要
我们提出了一种随机矩阵方法，用于研究使用相关的Wishart集合的转化不变性的稳定无定形固体的一般振动特性。在这种方法中，可以应用分析方法和数值方法。使用随机矩阵理论，我们发现了状态振动密度的分析形式和动态结构因子。我们证明了在较高频率下的低频传播声子和扩散子之间存在Ioffe-Regel交叉的存在。状态的振动密度降低显示玻色子峰，该频率接近Ioffe-Regel交叉。我们还提出了一个具有有限相互作用半径的简单数值随机矩阵模型，该模型的性质迅速收敛到分析结果，并增加了相互作用半径。对于良好的相互作用半径，数值模型证明了具有幂律状态低频密度的准化振动的存在。
We present a random matrix approach to study general vibrational properties of stable amorphous solids with translational invariance using the correlated Wishart ensemble. Within this approach, both analytical and numerical methods can be applied. Using the random matrix theory, we found the analytical form of the vibrational density of states and the dynamical structure factor. We demonstrate the presence of the Ioffe-Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, which frequency is close to the Ioffe-Regel crossover. We also present a simple numerical random matrix model with finite interaction radius, which properties rapidly converges to the analytical results with increasing the interaction radius. For fine interaction radius, the numerical model demonstrates the presence of the quasilocalized vibrations with a power-law low-frequency density of states.
