Effective interactions of ultracold bosons in anisotropic and anharmonic potentials

We have recently calculated effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in an isotropic (spherical) harmonic trap. But for the important case of optical lattice potentials these results provide only a rough estimate of the effective multibody interactions in the small scattering length regime. In this talk I will extend our model and results to anisotropic and anharmonic potentials. For example, we find anharmonic corrections as large as 30-40{\%} for the effective three-body interaction strength in typical optical lattice potentials. I also discuss non-perturbative behaviors of the multibody interactions.