Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations—often called “soft spots”—that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes—coined here nonlinear quasilocalized excitations (NQEs)—that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

中文翻译：

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玻璃中的非线性准局域激发：柔点的真实代表

通过将熔体淬火形成的结构玻璃具有大量的准局部软激发（通常称为“软点”），这些激发被认为在各种热力学，传输和机械现象中起关键作用。在狭窄的情况下，准局部激发采取振动（正态）模式的形式，可以通过对多维势能的谐波分析轻松获得。但是，总的来说，与其他低能激发（例如声子）的杂交阻碍了通过谐波分析直接进入准局部化模式的群体。在本系列文章中，我们重新介绍和研究一类低能量准局部化模式的统计力学性质，在这里产生了非线性准局部化激励（NQE）-通过对玻璃的势能图进行非谐（非线性）分析来定义，并且不与其他低能激发杂交。在本文中，我们回顾了嵌入NQE的微机械定义的理论框架。我们演示了谐波准局部化模式如何与其他软激励混合，而NQE正确地代表了软点而不进行杂交。我们显示NQE的能量收敛到最软，非杂化谐波准局部化模式的能量，巩固了它们作为结构玻璃软斑的真实代表的地位。最后，我们对NQE的机械性能进行统计分析，从而对围绕结构玻璃的典型固有状态的势能垒的分布进行了预测，