Non-Hermitian superintegrable systems

Abstract

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.