Mean-field model of interacting quasilocalized excitations in glasses

TL;DR

This paper introduces a mean-field model for quasilocalized excitations in glasses, explaining the universal $ ext{DOS} \, ext{~} \, ext{omega}^4$ behavior and analyzing how interactions influence the density of states and characteristic frequencies.

Contribution

The study presents a novel mean-field model capturing the universal $ ext{omega}^4$ density of states in glasses and provides a detailed analysis of how interaction parameters affect this behavior.

Findings

The model produces a gapless density of states with $ ext{omega}^4$ scaling.

The prefactor $A_g$ varies nonmonotonically with interaction strength $J$.

$A_g$ exhibits exponential decay in weak interaction regimes and power-law decay at stronger interactions.

Abstract

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.