Due to the topological disorder, glass displays an anomalous vibrational density of states beyond the Debye model, i.e., formation of boson peaks, which is fundamental for understanding many glassy physical properties. However, the understanding of the boson peak remains notoriously complex and is a topic of hot debate. Here we report a universal quantitative relation between boson peak intensity and the Debye level of transverse phonons in different glasses, confirming the intrinsic link between boson peaks and transverse phonons. Moreover, an equation is derived for the boson peak intensity and Debye-Waller factor, indicating that boson peaks are fundamentally determined by the Debye-Waller factor. These findings could clarify some controversial issues and reveal a common basis for high-frequency boson peak dynamics $(\sim {10}^{12}\mathrm{Hz})$, short-time $\beta$ processes $({10}^3\sim {10}^6\mathrm{Hz})$, and long-time $\alpha$ processes $({10}^{-4}\sim {10}^3\mathrm{Hz})$ in disordered materials.

中文翻译：

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玻色子峰与无序材料中德拜能级和德拜-沃勒因子的普遍关系

由于拓扑混乱，玻璃显示出超出Debye模型的异常振动密度状态，即形成玻色子峰，这对于理解许多玻璃态物理性质至关重要。然而，对玻色子峰的理解仍然非常复杂，并且是热门话题。在这里，我们报告了玻色子峰值强度和横向声子在不同玻璃中的德拜能级之间的普遍定量关系，证实了玻色子峰和横向声子之间的内在联系。此外，推导了玻色子峰强度和德拜-沃勒因子的方程式，表明玻色子峰从根本上由德拜-沃勒因子确定。这些发现可能会澄清一些有争议的问题，并揭示高频玻色子峰动力学的共同基础。$（〜{10}^{12}\mathrm{赫兹}）$， 短时间 $\beta$ 流程 $（{10}^3〜{10}^6\mathrm{赫兹}）$和长时间 $\alpha$ 流程 $（{10}^{-4}〜{10}^3\mathrm{赫兹}）$ 在无序的材料中。