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arXiv 1610.03410cond-mat.soft
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结构玻璃中的非线性模使玻璃模和Goldstone模分离

Nonlinear modes disentangle glassy and Goldstone modes in structural glasses

Luka Gartner, Edan Lerner

摘要:

玻璃态固体物理学中的一个突出问题是理解低能量激发的统计和性质,这些激发源于表征这些系统微观结构的无序。在这项工作中,我们介绍了一个家庭的代数方程组,其解决方案代表集体位移方向(模式)在多维配置空间的结构玻璃。我们解释了为什么解决方案的代数方程,创造非线性玻璃模式,是准本地化的低能量激发。我们提出了一种迭代方法来解决的代数方程组,并用它来研究的能量和结构特性的一个选定的子集,他们的解决方案,从正常模式分析的模型玻璃的势能。我们的关键结果是,与谐波玻璃振动模式和它们的非线性对应物的结构和能量收敛在非常低的频率的限制。由于非线性模式从来没有遭受杂交,我们的研究结果意味着,所提出的理论框架构成了一个强大的替代定义的“软玻璃模式”的热力学极限,其中戈德斯通模式压倒和破坏的身份,低频谐波玻璃模式。

英文摘要:

One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a family of algebraic equations whose solutions represent collective displacement directions (modes) in the multi-dimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasi-localized low-energy excitations. We present an iterative method to solve the algebraic equations, and use it to study the energetic and structural properties of a selected subset of their solutions constructed by starting from a normal mode analysis of the potential energy of a model glass. Our key result is that the structure and energies associated with harmonic glassy vibrational modes and their nonlinear counterparts converge in the limit of very low frequencies. As nonlinear modes never suffer hybridizations, our result implies that the presented theoretical framework constitutes a robust alternative definition of `soft glassy modes' in the thermodynamic limit, in which Goldstone modes overwhelm and destroy the identity of low-frequency harmonic glassy modes.

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