Motivated by the recent experiments studying Bose-Einstein condensates
of trapped ultracold atomic gases in an optical lattice
(Greiner et al., Nature 415, 39 (2002)), I plan to
investigate the quantum phase transition
between the Mott insulating phase and the superfluid phase.
In particular, I will focus on the non-equilibium aspects as well as
on the influence of the finite geometry due to the presence of the
confinfing potential.