The evolution of vibrational excitations in glassy systems

TL;DR

This paper uses mode-coupling theory to analyze vibrational excitations in glassy systems, revealing how density fluctuations and the boson peak influence high-frequency sound and elastic properties.

Contribution

It demonstrates how the interaction between density fluctuations and the glass structure leads to the boson peak and high-frequency sound, providing a theoretical framework for these phenomena.

Findings

Identification of the boson peak as an anomalous-oscillation peak

Derivation of high-frequency sound properties consistent with experiments

Validation of schematic MCT models as approximations

Abstract

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.