Non-hermitian models in higher dimensions

Abstract

It is know that PT-symmetric models have real spectra provided the symmetry is not spontaneously broken. Even pseudo-hermitian models have real spectra, which enlarge the the class of non-hermitian models possessing real spectra. We however consider non-hermitian models in higher dimensions which are not necessarily explicit PT-symmetric nor pseudo-hermitian. We show that the models may generate real spectra depending upon the coupling constants of the Hamiltonian. Our models thus further generalize the class of non-hermitian systems, which possess real spectra.