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Open Quantum Systems Decoherence

The quantum harmonic oscillator on a circle - fragmentation of the algebraic method

arXiv
Authors: Daniel Burgarth, Paolo Facchi

Year

2026

Paper ID

35751

Status

Preprint

Abstract Read

~2 min

Abstract Words

60

Citations

N/A

Abstract

A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument - implying integer gaps - fails. The answer is illuminating and covers a surprisingly rich range of physical phenomena for such a simple model.

Why This Paper Matters

  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.23774 [2] arXiv https://arxiv.org/abs/2603.23774 [3] Publisher https://arxiv.org/abs/2603.23774

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