Vibrations and Relaxations in a Soft Sphere Glass: Boson Peak and Structure Factors

TL;DR

This study investigates vibrational dynamics in a soft sphere glass, revealing a pronounced boson peak, the nature of transverse vibrations, and the behavior of phonons and structure factors across different regimes.

Contribution

It provides new insights into the vibrational density of states, phonon damping, and structure factors in a soft sphere glass, linking collective motions to local relaxations.

Findings

Boson peak matches universal form for soft oscillators.

Transverse vibrations dominate the excess modes.

Transverse phonons become over-damped near the boson peak.

Abstract

The dynamics of a soft sphere model glass, studied by molecular dynamics, is investigated. The vibrational density of states divided by $\omega^2$ shows a pronounced boson peak. Its shape is in agreement with the universal form derived for soft oscillators interacting with sound waves. The excess vibrations forming the boson peak have mainly transverse character. From the dynamic structure factor in the Brillouin regime pseudo dispersion curves are calculated. Whereas the longitudinal phonons are well defined up to the pseudo zone boundary the transverse ones rapidly get over-damped and go through the Ioffe-Regel limit near the boson peak frequency. In the high $q$ regime constant-$\omega$ scans of the dynamic structure factor for frequencies around the boson peak are clearly distinct from those for zone boundary frequencies. Above the Brillouin regime, the scans for the low frequency modes follow closely the static structure factor. This still holds after a deconvolution of the exact harmonic eigenmodes into local and extended m odes. Also the structure factor for local relaxations at finite temperatures resembles the static one. This semblance between the structure factors mirrors the collective motion of chain like structures in both low frequency vibrations and atomic hopping processes, observed in the earlier investigations.