Character of Atomic Vibrations in a Lennard-Jones Glass

TL;DR

This study investigates atomic vibrational modes in Lennard-Jones glasses using harmonic approximation, revealing that modes are primarily distinguished by eigenfrequency with localized and delocalized states, and transverse or longitudinal character is indistinguishable within narrow frequency ranges.

Contribution

It provides a detailed analysis of vibrational eigenmodes in Lennard-Jones glasses, highlighting the frequency-based classification and the uniformity of mode properties within narrow frequency intervals.

Findings

7% of modes are localized, rest are delocalized

Modes cannot be distinguished by properties other than eigenfrequency

Transverse and longitudinal characters are indistinguishable in narrow frequency ranges

Abstract

Lennard-Jones glasses (made on a computer by quenching from liquid state coordinates) are studied in harmonic approximation. Vibrational eigenfrequencies and eigenvectors are found by exact diagonalization for models with periodic boundaries and N=(500, 2048, and 6980) atoms. We analyze the density of states, mobility edge, and bond-stretching character of the normal modes. In agreement with older work of Grest, Nagel, and Rahman, the upper 7% of modes are localized, and the rest, delocalized. We find that modes can not be differentiated by any property or quantum number except their eigenfrequency. More specifically, in a given narrow frequency interval, all modes are globally identical. Transverse or longitudinal character, for example, disappears.