Quantum dynamics of coupled bosonic wells within the Bose-Hubbard picture

We relate the quantum dynamics of the Bose-Hubbard model (BHM) to the semic lassical nonlinear equations that describe an array of interacting Bose con densates by implementing a standard variational procedure based on the cohe rent state method. We investigate the dynamics of the two-site BHM from the purely quantum viewpoint by recasting first the model within a spin pictur e and using then the related dynamical algebra. The latter allows us to stu dy thoroughly the energy spectrum structure and to interpret quantally the classical symmetries of the two-site dynamics. The energy spectrum is also evaluated through various approximations relying on the coherent state appr oach.