论文标题
3D玻璃中第一个声音模式以下状态的密度
Density of States below the First Sound Mode in 3D Glasses
论文作者
论文摘要
玻璃具有普遍的低频过量振动模式，超出了Debye预测，这可以有助于合理化，例如，与晶体固体相比，玻璃杯对热性能的异常温度依赖性。这些低频多余模式$ d（ω）$的状态密度取决于频率$ω$数十年来一直在争论。对3D眼镜的最新模拟研究表明，在低频制度下，$ d（ω）$ scales在低频制度中普遍使用$ω^4 $。但是，尚无模拟研究曾尽可能低频率来直接测试该四分法是否可以一直运行到极低的频率。在这里，我们计算出在频率范围的3D眼镜中的第一个声音模式以下的$ d（ω）$。我们发现$ d（ω）$ scales在非常低的频率下使用$ω^β$，$β<4.0 $，而$ω^4 $ Law仅在某些眼镜中的中间频率中工作。此外，我们的进一步分析表明，我们的观察结果不取决于所检查的玻璃模型或玻璃稳定性。在第一个声音模式下方的$ d（ω）$的$ω^4 $定律在当前对3D眼镜的模拟研究中占主导地位，而我们直接观察到非常低的频率的四分法分解，因此留下了一个开放但重要的问题，这可能会吸引更多未来的数字和理论研究。
Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses' unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes $D(ω)$ depends on the frequency $ω$ has been debated for decades. Recent simulation studies of 3D glasses suggest that $D(ω)$ scales universally with $ω^4$ in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated $D(ω)$ below the first sound mode in 3D glasses over a wide range of frequencies. We find $D(ω)$ scales with $ω^β$ with $β<4.0$ at very low frequencies examined, while the $ω^4$ law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The $ω^4$ law of $D(ω)$ below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.
