Universality in the vibrational spectra of weakly-disordered two-dimensional clusters

TL;DR

This study numerically analyzes vibrational spectra of two-dimensional weakly-disordered clusters, revealing universal spectral features and mode properties that align with random matrix theory predictions, similar to three-dimensional systems.

Contribution

It demonstrates that the vibrational density of states and fluctuation properties in 2D clusters exhibit universality and convergence to random matrix theory, extending prior 3D findings.

Findings

Density of states approaches a universal form as well width decreases

Most vibrational modes are extended, with fewer degrees involved compared to 3D

Mode fluctuations match Gaussian orthogonal ensemble predictions

Abstract

We numerically investigate the vibrational spectra of single-component clusters in two-dimensions. Stable configurations of clusters at local energy minima are obtained, and for each the hessian matrix is evaluated and diagonalized to obtain eigenvalues as well as eigenvectors. We study the density of states so obtained as a function of the width of the potential well describing the two-body interaction. As the width is reduced, as in three dimensions, we find that the density of states approaches a common form, but the two-peak behavior survives. Further, calculations of the participation ratio show that most states are extended, although a smaller fraction of the degrees of freedom are involved in these modes, compared to three dimensions. We show that the fluctuation properties of these modes converges to those of the Gaussian orthogonal ensemble of random matrices, in common with previous results on three dimensional amorphous clusters and molecular liquids