Localization of particles in harmonic confinement: Effect of the interparticle interaction

TL;DR

This paper investigates how particles confined in a 2D harmonic trap localize under rotation, comparing quantum spectra for different particle types and interaction ranges, revealing vibrational modes as key to understanding high-angular-momentum behavior.

Contribution

It introduces a detailed quantum mechanical analysis of particle localization in harmonic traps, highlighting the role of vibrational modes across particle types and interaction ranges.

Findings

Localization is similar for bosons and fermions at small particle numbers.

Quantum spectra at high angular momentum are explained by vibrational modes.

Interaction range does not significantly alter the localization behavior.

Abstract

We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation and vibrational modes of localized particles. We show that for a small number of particles the localization is similar for bosons and fermions. Moreover, independent of the range of the interaction the quantum mechanical spectrum at large angular momenta can be understood by vibrational modes of localized particles.