Non-Hermitian superintegrable systems

• URL: http://arxiv.org/abs/2304.01039v1
• Date: Mon, 3 Apr 2023 14:43:57 GMT
• Title: Non-Hermitian superintegrable systems
• Authors: Francisco Correa, Luis Inzunza, Ian Marquette
• Abstract summary: A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $mathcalPT$-symmetric superintegrable models. The mechanism is illustrated with one- and two-dimensional examples, related to $u(2)$ and $u(3)$ Lie algebras respectively. In certain limits, the models reduce to known non-Hermitian systems and complex extensions of previously studied real superintegrable systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum $\mathcal{PT}$-symmetric superintegrable models over an $n$-dimensional sphere $S^n$. The mechanism is illustrated with one- and two-dimensional examples, related to $u(2)$ and $u(3)$ Lie algebras respectively, providing new quantum models with real spectra and spontaneous $\mathcal{PT}$-symmetric breaking. In certain limits, the models reduce to known non-Hermitian systems and complex extensions of previously studied real superintegrable systems.

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