The spectrum of a non-Hermitian two-mode Bose-Hubbard system

We study an N-particle, two-mode Bose-Hubbard system, modelling a Bose-Einstein condensate in a double-well potential. By introducing effective complex energies to the modes we describe a coupling to a continuum. The eigenvalues of the resulting non-Hermitian matrix model are in general complex where the imaginary parts (resonance widths) describe the decay rate into the continuum. In dependence on the system parameters, the eigenvalues show intricate patterns of avoided and real crossings, as well as characteristic bifurcations. In the present talk the effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analysed and its peculiarities are clarified by perturbational methods.