Analysis of vibrational normal modes for Coulomb clusters

TL;DR

This paper investigates the vibrational normal modes of Coulomb clusters in two-dimensional irregular confinement, revealing their localized, quasi-localized, and delocalized nature, and linking low-frequency modes to particle dynamics.

Contribution

It introduces a novel correlation function to analyze the spatial structure of vibrational modes and connects these modes to particle dynamics at low temperatures.

Findings

Modes are characterized as localized, quasi-localized, or delocalized.

Low-frequency quasi-localized modes correlate with particle displacements.

Characteristic length scales of modes are extracted from the correlation function.

Abstract

We study various properties of the vibrational normal modes for Coulomb-interacting particles in two-dimensional irregular confinement using numerical simulations. By analyzing the participation ratio and spectral statistics, we characterize the vibrational modes for Coulomb clusters as localized, quasi-localized and delocalized. We also study a novel correlation function to understand the spatial structure of these different kinds of modes and subsequently extract the associated characteristic length scales. We further demonstrate that, at any given temperature, particles exhibiting larger displacement over a time interval comparable to the structural relaxation time, are strongly correlated with the low-frequency quasi-localized modes of the inherent structure corresponding to the initial configuration. Establishing this correlation for Coulomb clusters paves the path to identify the particular feature of the initial configuration that determines the previously observed heterogeneous dynamics of the particles at low temperatures in these systems.