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arXiv · 2310.01191

Unveiling Symmetries Patterns: A Study of Circular and Linear Harmonic Oscillator Chains

Edoardo Spezzano·Alberto Iommi
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Abstract

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 $\mathbb{Z}_2$ group structure arises in both problems, showing how a degenerate spectrum in the circular case is attributable to the specific geometry producing a $\mathbb{Z}_N$ symmetry.

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Edoardo Spezzano, Alberto Iommi. 2023-10-02. Unveiling Symmetries Patterns: A Study of Circular and Linear Harmonic Oscillator Chains. https://arxiv.org/abs/2310.01191

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