Analysis of vibrational normal modes for Coulomb clusters

Abstract

We study various properties of the vibrational normal modes for Coulomb-interacting particles in twodimensional 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.

A localization transition underlies the mode-coupling crossover of glasses

“…It will be interesting to analyze this connection in future work. A well-established method to distinguish localized and delocalized modes builds on the analysis of the level spacing statistics [54], as used extensively in the analysis of spectra in a variety of problems, including the INM of supercooled and confined liquids [47,55,56]. Here we compute the level spacing distribution of stationary and quasi-stationary points of the PES.…”

Renormalization to localization without a small parameter

“…Although such models sometimes arise in the systems with shortrange interactions, such as elastic networks [39], jammed soft spheres [40] or magnetic vortex plasma [41], more commonly ERMs are used to describe the long-range models. Indeed, longrange ERMs are applied to the analysis of the systems of particles with Coulomb interactions in two-dimensional irregular confinement [42], disordered classical Heisenberg magnets with uniform antiferromagnetic interactions [43], systems with dipole-dipole interactions such as dipolar gases [44], systems of ultracold Rydberg atoms [45] and so on. Even the effects of photon localization in atomic gases [46] are described by a long-range ERM.…”