Regular Seminar Eva-Maria Graefe (Technische Universitaet Kaiserslautern)
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 parameters the spectrum shows an intricate structure of exceptional points, at which two or more eigenvalues as well as the corresponding eigenstates are degenerate. In the present talk the effect of the interplay between the particle interaction and the non-Hermiticity on the spectrum is analysed, drawing special attention to the occurrence and unfolding of exceptional points. Some peculiarities are clarified using perturbational methods.