Corrado Rainone, Pierfrancesco Urbani, Francesco Zamponi, Edan Lerner, and Eran Bouchbinder
SciPost Phys. Core 4, 008 (2021) ·
published 16 April 2021

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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 yet fully understood. Here we study a meanfield 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 nonuniversal prefactor $A_{\rm g}(h,J,\kappa_0)$, of the oscillators' interactioninduced 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 decays as a powerlaw 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.
SciPost Phys. 1, 016 (2016) ·
published 31 December 2016

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One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the lowenergy 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 multidimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasilocalized lowenergy 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 lowfrequency harmonic glassy modes.
Dr Lerner: "We thank the referee for caref..."
in Submissions  report on Nonlinear modes disentangle glassy and Goldstone modes in structural glasses