Complex Higgs Oscillators

Abstract

In this note we discuss the complex version of the Higgs oscillator on the hyperbolic space. The eigenvalues and resonances of the complex Higgs oscillator are computed in different examples in the hyperbolic setting. We also propose open problems like whether the complex absorbing potential (CAP) method works for asymptotically hyperbolic manifolds and finding hyperbolic analogues of the complex harmonic oscillator.