Integrability of interacting two-level boson systems

We prove that a wide class of two-level boson systems interacting through k-body forces is integrable in the semiclassical limit irrespective of the value of the parameters of the model. This class of models includes number-conserving Hamiltonians, and interactions which do not conserve the particle number. Applications to two-component and atom-molecule Bose-Einstein condensates at zero temperature as well as to the bosonic k-body embedded ensembles of Gaussian random matrices in the dense limit are discussed.