arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.11793cond-mat.mtrl-scicond-mat.dis-nn
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玻璃中的弹性异常:甘油和二氧化硅情况下的弦论理解

Elastic anomalies in glasses: the string theory understanding in the case of Glycerol and Silica

Ernesto Bianchi, Valentina M. Giordano, Fernando Lund

摘要:

我们提出了一个实施的分析弦论最近应用到描述的玻璃。这些被建模为连续介质与嵌入的弹性弦不均匀性,随机定位和随机取向,它振荡的直平衡位置与基频取决于它们的长度。长度分布的存在反映了振荡频率的分布,这是玻璃态密度中玻色子峰的原因。以前,它已被证明,这样的描述可以解释弹性异常报告的频率与玻色子峰。本文从广义流体力学出发,确定了由音串干涉产生的相干、色散和衰减的声波的动态关联函数$S(k,ω)$。一旦测量了振动态密度,我们就可以用它来明确地确定给定玻璃固有的弦长度分布。使用这种分布得到的密度-密度关联函数是强约束的,并且能够解释在两种原型玻璃上收集的实验数据:甘油和二氧化硅。所得到的字符串长度分布是兼容的弹性不均匀性的典型尺寸先前报道的二氧化硅和过冷液体,和与字符串动力学的原子运动是一致的,最近确定的软模式在大规模的数值模拟作为非声子模式负责玻色子峰。因此,该理论与玻璃特定动力学的最新进展相一致,并提供了对后者微观起源的简单理解,同时提出了关于弦分布性质的普遍性或材料特异性的新问题。

英文摘要:

We present an implementation of the analytical string theory recently applied to the description of glasses. These are modeled as continuum media with embedded elastic string heterogeneities, randomly located and randomly oriented, which oscillate around a straight equilibrium position with a fundamental frequency depending on their length. The existence of a length distribution reflects then in a distribution of oscillation frequencies which is responsible for the Boson Peak in the glass density of states. Previously, it has been shown that such a description can account for the elastic anomalies reported at frequencies comparable with the Boson Peak. Here we start from the generalized hydrodynamics to determine the dynamic correlation function $S(k,ω)$ associated with the coherent, dispersive and attenuated, sound waves resulting from a sound-string interference. Once the vibrational density of states has been measured, we can use it for univocally fixing the string length distribution inherent to a given glass. The density-density correlation function obtained using such distribution is strongly constrained, and able to account for the experimental data collected on two prototypical glasses: glycerol and silica. The obtained string length distribution is compatible with the typical size of elastic heterogeneities previously reported for silica and supercooled liquids, and the atomic motion associated to the string dynamics is consistent with the soft modes recently identified in large scale numerical simulations as non-phonon modes responsible for the Boson Peak. The theory is thus in agreement with the most recent advances in the understanding of the glass specific dynamics and offers an appealing simple understanding of the microscopic origin of the latter, while raising new questions on the universality or material-specificity of the string distribution properties.

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