Non-Hermitian superintegrable systems

A non-Hermitian generalisation of the Marsden–Weinstein reduction method is introduced to construct families of quantum -symmetric superintegrable models over an n-dimensional sphere Sn. 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 -symmetric breaking. In certain limits, the models reduce to known non-Hermitian systems and complex extensions of previously studied real superintegrable systems.

Note:

18 pages, no figures

non-Hermitian Hamiltonians
superintegrable systems
𝒫𝒯-symmetry
Marsden–Weinstein reduction

References(76)

Figures(0)

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