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This paper analyzes dynamical properties of small Fermi-Hubbard andBose-Hubbard systems, focusing on the structure of the underlying Hilbertspace. We evaluate time-dependent quantities such as the return probability tothe initial state and the spin imbalance of spin-1/2 fermions. The results arecompared with recent experimental observations in ultracold gases. For thesymmetric two-site Fermi-Hubbard model we find that the spin imbalance and thereturn probability are controlled by two and three frequencies, respectively.The spin imbalance and the return probability are identical for the asymmetricFalicov-Kimball limit and controlled by only one frequency. In general, thetransition probabilities between the initial state and energy eigenstatesdepend strongly on the particle-particle interaction. This is discussed for"self trapping" of spinless bosons in a double-well potential. We observe thatthe available Hilbert space is reduced significantly by strong interaction.

Dynamics of finite Fermi-Hubbard and Bose-Hubbard systems