Lerner Edan
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, the Netherlands.
Phys Rev E. 2020 Mar;101(3-1):032120. doi: 10.1103/PhysRevE.101.032120.
The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency ω in structural glasses, D(ω), was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, D(ω) increases from zero frequency as ω^{4}, independent of spatial dimension and of microscopic details. However, it has been shown [Lerner and Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)2470-004510.1103/PhysRevE.96.020104] that the preparation protocol employed to create glassy samples may affect the form of their resulting D(ω): glassy samples rapidly quenched from high-temperature liquid states were shown to feature D(ω)∼ω^{β} with β<4, presumably limiting the degree of universality of the ω^{4} law. Here we show that exponents β<4 are seen only in small glassy samples quenched from high-temperature liquid states-whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations-while larger glassy samples made with the same protocol feature the universal ω^{4} law. Our results demonstrate that observations of β<4 in the nonphononic density of states stem from finite-size effects, and we thus conclude that the ω^{4} law should be featured by any sufficiently large glass quenched from a melt.
几十年前，人们从理论上预测了结构玻璃中频率为ω的非声子、准局域振动模式密度的通用形式D(ω)，但直到最近才在数值模拟中得以揭示。特别是，最近已经确定，在一般的计算机玻璃中，D(ω)从零频率开始随ω^4增加，与空间维度和微观细节无关。然而，[勒纳和布赫宾德，《物理评论E》96, 020104(R) (2017)2470 - 004510.1103/PhysRevE.96.020104]表明，用于制备玻璃态样品的制备方案可能会影响其最终D(ω)的形式：从高温液态快速淬火的玻璃态样品显示出D(ω)∼ω^β，其中β<4，这可能限制了ω^4定律的普遍性程度。在这里，我们表明，β<4的指数仅出现在从高温液态淬火的小玻璃态样品中——其尺寸与软准局域振动的无序核心尺寸相当或更小——而用相同方案制备的较大玻璃态样品具有通用的ω^4定律。我们的结果表明，在非声子态密度中观察到β<4源于有限尺寸效应，因此我们得出结论，任何从熔体淬火的足够大的玻璃都应具有ω^4定律。
