  We present a theoretical study of bose condensation and specific heat of
non-interacting bosons in finite lattices in harmonic potentials in one, two,
and three dimensions. We numerically diagonalize the Hamiltonian to obtain the
energy levels of the systems. Using the energy levels thus obtained, we
investigate the temperature dependence, dimensionality effects, lattice size
dependence, and evolution to the bulk limit of the condensate fraction and the
specific heat. Some preliminary results on the specific heat of fermions in
optical lattices are also presented. The results obtained are contextualized
within the current experimental and theoretical scenario.
