Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185, Rome, Italy.
ISC-CNR, Institute for Complex Systems, Piazzale A. Moro 2, I-00185 Rome, Italy.
Phys Rev Lett. 2019 Oct 11;123(15):155502. doi: 10.1103/PhysRevLett.123.155502.
Recent numerical studies on glassy systems provide evidence for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states D(ω). Similarly to Goldstone modes (GMs), i.e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature T^{} modifies the GM/NGM ratio in D(ω). In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent s(T^{}) in the low-frequency power law D(ω)∼ω^{s(T^{})}, with 2≤s(T^{})≤4. Second, by comparing s(T^{}) with s(p), i.e., the same quantity obtained by pinning a p particle fraction, we suggest that s(T^{}) reflects the presence of dynamical heterogeneous regions of size ξ^{3}∝p. Finally, we provide an estimate of ξ as a function of T^{}, finding a mild power law divergence, ξ∼(T^{}-T_{d})^{-α/3}, with T_{d} the dynamical crossover temperature and α falling in the range α∈[0.8,1.0].
最近对玻璃态系统的数值研究提供了证据，表明在振动态密度 D(ω)的低频谱中存在非戈德斯通模式（NGM）的群体。与固体中的声子（GM）即戈德斯通模式类似，NGM 是软的低能量激发态。然而，与 GM 不同，NGM 是局域激发态。在这里，我们首先表明母体温度 T^{} 会改变 D(ω)中的 GM/NGM 比值。具体来说，声子衰减反映在低频幂律 D(ω)∼ω^{s(T^{})}中母体温度依赖性的指数 s(T^{})中，其中 2≤s(T^{})≤4。其次，通过比较 s(T^{})和 s(p)，即通过钉扎 p 粒子分数得到的相同数量，我们表明 s(T^{})反映了存在大小 ξ^{3}∝p 的动力学不均匀区域。最后，我们提供了一个关于 T^{}的 ξ 的估计值，发现一个温和的幂律发散，ξ∼(T^{}-T_{d})^{-α/3}，其中 T_{d}是动力学交叉温度，α 落在 0.8 到 1.0 之间。
