Scattering Properties of Bose-Hubbard Hamiltonians with Two and Three Sites

We consider a probe particle in a tight binding geometry with two leads and a central site that is coupled to a Bose-Hubbard system consisting of two or three wells (dimer/trimer). In the case of the dimer we find that the resonance widths undergo a sequence of bifurcations resulting from the complexity of the underlying classical phase space structure. For the trimer we show that the statistical properties of the scattering matrix are well described by the random matrix theory predictions for chaotic scattering. The origin of this agreement is due to the fact that inelastic scattering from a chaotic system (trimer) is formally equivalent to elastic scattering in a waveguide that has a chaotic mode space.