The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden Z2 group structure arises in both problems, showing how a degenerate spectrum in the circular case is attributable to the specific geometry producing a ZN symmetry.
@article{arxiv.2310.01191,
title = {Unveiling Symmetries Patterns: A Study of Circular and Linear Harmonic Oscillator Chains},
author = {Edoardo Spezzano and Alberto Iommi},
journal= {arXiv preprint arXiv:2310.01191},
year = {2023}
}