玻璃中的波衰减：瑞利和广义瑞利散射定标
Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling
摘要：
玻璃无序对长波声子（波）的衰减在各种玻璃异常中起着核心作用，但它既没有完全表征，也没有完全理解。特别重要的是在宏观玻璃的热力学极限中，用小的波数$k\!\to\!0$缩放衰减率$Γ(k)$。在这里，我们使用的理论和广泛的计算机模拟相结合，以表明宏观低频行为出现在中频有限尺寸的玻璃，以上最近确定的交叉波数$k_\dagger$，声子不再量化成带。对于$k\!<\!k_\dagger$，有限尺寸效应占主导地位的$Γ(k)$，这是定量描述的无序声子带的理论。对于$k\!>\!k_\dagger$，我们发现，$Γ(k)$是受准定域非声子激发，一个通用的签名的玻璃，具有普遍的状态密度的数量。特别是，我们表明，在一个频率范围内，这个数字是小的，$Γ(k)$遵循瑞利散射缩放$\sim\!k^{d+1}$（$d$是空间维度），并在一个频率范围内，这个数字是足够大的，最近观察到的广义瑞利缩放的形式$\sim\!k^{d+1}\log\!{(k_0/k)}$出现（$k_0\!>k_\dagger$是一个特征波数）。我们的研究结果表明，宏观玻璃--，特别是，传统的实验室淬火，被称为强烈抑制准本地化非声子激发产生的玻璃-表现出瑞利标度在最低波数$k$和交叉广义瑞利标度在较高的$k$。一些支持的实验证据，从最近的文献。
英文摘要：
The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $Γ(k)$ with small wavenumbers $k\!\to\!0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_\dagger$, where phonons are no longer quantized into bands. For $k\!<\!k_\dagger$, finite-size effects dominate $Γ(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k\!>\!k_\dagger$, we find that $Γ(k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $Γ(k)$ follows a Rayleigh scattering scaling $\sim\!k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim\!k^{d+1}\log\!{(k_0/k)}$ emerges ($k_0\!>k_\dagger$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.
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