  In the present paper, we investigate the dynamics of a Bose-Einstein
condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both
analytically and numerically. We focus on the self-trapping state and the
effect of the system dimension. Under the tight-binding approximation we obtain
an analytical criterion for the self-trapping state of BEC using time-dependent
variational method. The phase diagram for self-trapping, soliton, breather, or
diffusion of the BEC cloud is obtained accordingly and verified by directly
solving the discrete Gross-Pitaevskii equation (GPE) numerically. In
particular, we find that the criterion and the phase diagrams are modified
dramatically by the dimension of the lattices.
