Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel.
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
J Chem Phys. 2019 Sep 14;151(10):104503. doi: 10.1063/1.5111192.
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 → 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, where phonons are no longer quantized into bands. For k < k, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k, 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 ∼k (¯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 ∼k log(k/k) emerges (k > k 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.
长波声子（波）在玻璃无序中的衰减在各种玻璃异常中起着核心作用，但它既没有被完全描述，也没有被完全理解。特别重要的是，在宏观玻璃的热力学极限中，衰减率 Γ(k) 随小波数 k→0 的标度。在这里，我们使用理论和广泛的计算机模拟相结合的方法，表明宏观低频行为出现在有限尺寸玻璃的中间频率之上，在最近确定的交叉波数 k 之上，在那里，声子不再被量化成能带。对于 k<k，有限尺寸效应主导 Γ(k)，这可以通过无序声子带的理论来定量描述。对于 k>k，我们发现 Γ(k)受到准局域非声子激发数量的影响，这是具有通用态密度的玻璃的通用特征。特别是，我们表明，在准局域非声子激发数量较小的频率范围内，Γ(k)遵循瑞利散射标度∼k（¯d 是空间维度），并且在准局域非声子激发数量足够大的频率范围内，最近观察到的广义瑞利散射形式∼k log(k/k)出现（k>k 是一个特征波数）。我们的结果表明，宏观玻璃，特别是那些通过已知强烈抑制准局域非声子激发的常规实验室淬火生成的玻璃，在最低波数 k 处表现出瑞利散射，在更高波数 k 处表现出广义瑞利散射的交叉。我们还提出了一些来自最近文献的支持性实验证据。
