Variational dynamics of Bose-Einstein condensates in deep optical lattices

We study the dynamics of a Bose-Einstein condensate wavepacket trapped in an optical lattice. In the tight-binding limit, the system maps onto a discrete nonlinear Schrodinger equation. Using a collective coordinate approximation, we investigate different dynamical regimes: diffusive (in which the boson wavepacket spreads out), self-trapped (with a self-induced pinning), breathing (where the centre of mass of the wavepacket moves with an oscillating width), and solitonic (in which the wavepacket shape is exactly preserved during the dynamics).