We investigate the low-frequency spectrum in a three-dimensional model of structural glass focusing on small system sizes, and using different observables, i.e., the density of states $D\left(\omega \right)$, the cumulative of the density of states $F\left(\omega \right)$, and the dynamical structure factor $S(q,\omega )$ in the harmonic approximation. When the glass is obtained by an instantaneous quench from high temperatures, we show that extended “phonon-like” modes always populate the low-energy spectrum. Looking at the properties of the dynamical structure factor $S(q,\omega )$, we observe that in agreement with early studies of Lennard-Jones glasses [V. Mazzacurati, G. Ruocco, and M. Sampoli, Europhys. Lett. 34, 681 (1996)], there are still extended modes below the lowest resonant peak. These modes give rise to a plateau in the $S(q,\omega )$ for $\omega \to 0$. This result indicates that the low-energy spectrum of extended modes in glasses can be probed using small system sizes and performing instantaneous quench from high parental temperatures. As we recently observed [M. Paoluzzi, L. Angelani, G. Parisi, and G. Ruocco, Phys. Rev. Lett. 123, 155502 (2019)], the situation changes when the glassy configuration is obtained by an instantaneous quench from lower temperatures. The former protocol suppresses extended modes below the lowest resonant peak emphasizing the localized modes with $D\left(\omega \right)\sim {\omega }^4$.

中文翻译：

---

使用小型系统探测眼镜的德拜光谱

我们研究了结构玻璃的三维模型中的低频频谱，该模型关注较小的系统尺寸，并使用不同的可观测值，即状态密度 $d（\omega ）$，状态密度的累积 $F（\omega ）$，以及动力结构因素 $\mathrm{小号}（q，\omega ）$在谐波近似中 当通过高温瞬时淬火获得玻璃时，我们表明扩展的“声子状”模式始终会填充低能谱。看动力学结构因子的性质$\mathrm{小号}（q，\omega ）$，我们观察到与Lennard-Jones眼镜的早期研究一致[V. Mazzacurati，G。Ruocco和M. Sampoli，Europhys 。来吧 34，681（1996）]，有最低共振峰下面还是扩展模式。这些模式会导致$\mathrm{小号}（q，\omega ）$ 对于 $\omega \to 0$。该结果表明，可以使用较小的系统尺寸并从较高的父母温度进行瞬时淬灭来探测玻璃中扩展模式的低能谱。正如我们最近观察到的[M. Paoluzzi，L.Angelani，G.Parasi和G.Ruocco，物理学。牧师 123，155502（2019）]，当通过瞬时骤冷从较低的温度下得到的玻璃状配置情况的变化。前一种协议将扩展模式抑制到最低共振峰以下，着重强调了局部模式。$d（\omega ）〜{\omega }^4$。