玻璃中相互作用准局域激发的平均场模型

Corrado Rainone, Eran Bouchbinder, E. Lerner, P. Urbani, F. Zamponi
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引用次数: 19

摘要

结构玻璃具有准局域激发,其频率$\omega$遵循状态的普遍密度${\cal D}(\omega)\!\sim\!\omega^4$。然而,这种普适性背后的物理原理还没有被完全理解。在这里,我们研究了准局域激发在玻璃中的平均场模型,将其视为嵌入弹性介质中的粒子群,并将其统称为非谐振子。在没有相互作用的情况下,振子的谐波刚度取自一个相当无特征的概率分布(上截止$\kappa_0$),它们之间通过随机耦合(以强度为特征$J$)和与周围弹性介质(以恒定力为特征的相互作用$h$)相互作用。我们首先表明,该模型在广泛的模型参数范围内产生无间隙状态密度${\cal D}(\omega)\!=\!A_{\rm g}\,\omega^4$,以稳定非调和性的强度表示,这在模型中起决定性作用。然后,使用标度理论和数值模拟,我们提供了对非通用前因子$A_{\rm g}(h,J,\kappa_0)$,振荡器相互作用诱导的均方位移和新出现的特征频率的完整理解,所有这些都是根据正确识别的无量纲量。特别是,我们表明,对于固定的$h$, $A_{\rm g}(h,J,\kappa_0)$是$J$的非单调函数,在弱相互作用(小$J$)制度下,主要与$-(\kappa_0 h^{2/3}\!/J^2)$呈指数变化——让人想起最近在电脑眼镜上的观察——并且在$h$不起作用的制度下,对于较大的$J$,主要作为幂律衰减。我们讨论了该模型的物理解释及其与结构玻璃中现有观测结果的可能关系,并描绘了一些未来的研究方向。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mean-field model of interacting quasilocalized excitations in glasses
Structural glasses feature quasilocalized excitations whose frequencies $\omega$ follow a universal density of states ${\cal D}(\omega)\!\sim\!\omega^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $\kappa_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${\cal D}(\omega)\!=\!A_{\rm g}\,\omega^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{\rm g}(h,J,\kappa_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{\rm g}(h,J,\kappa_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(\kappa_0 h^{2/3}\!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.
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