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arXiv · 2304.01039

Non-Hermitian superintegrable systems

Francisco Correa·Luis Inzunza·Ian Marquette
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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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Francisco Correa, Luis Inzunza, Ian Marquette. 2023-04-03. Non-Hermitian superintegrable systems. https://doi.org/10.1088/1751-8121/ace506

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