论文标题
在低温下通过无序谐波振荡器捕获的玻璃振动现象
Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
论文作者
论文摘要
我们通过分析研究围绕随机位置谐波振荡的颗粒来研究拓扑无序材料的振动特性。在$ t = 0 $的热力学极限中利用经典田间理论，我们通过分析利用欧几里得随机矩阵理论的黑森来构建了一个自一致的模型。根据早期发现[T. S. Grigera等人〜STAT。〜MECH。通过这样做，我们最终获得了第一条原理理论，可以预测Athermal无序材料的主要异常，包括玻色峰，声音软化和声音的瑞利抑制作用。在状态的振动密度中，声音模式导致了debye定律的小频率。此外，在低频限制中以$ω^4 $开头的状态密度出现了多余，这归因于（准）局部模式。
We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at $T=0$, we build up a self-consistent model by analyzing the Hessian utilizing Euclidean Random Matrix theory. In accordance with earlier findings [T. S. Grigera et al.J.~Stat.~Mech.~11 (2011) P02015.], we take non-planar diagrams into account to correctly address multiple local scattering events. By doing so, we end up with a first principles theory that can predict the main anomalies of athermal disordered materials, including the boson peak, sound softening, and Rayleigh damping of sound. In the vibrational density of states, the sound modes lead to Debye's law for small frequencies. Additionally, an excess appears in the density of states starting as $ω^4$ in the low frequency limit, which is attributed to (quasi-) localized modes.
