  The quantum dynamics of one-dimensional bosonic Josephson junctions with
attractive and repulsive interparticle interactions is studied using the
Bose-Hubbard model and by numerically-exact computations of the full many-body
Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an
equivalence between the evolution in time of attractive and repulsive Josephson
junctions with attractive and repulsive interactions of equal magnitude. The
full many-body Hamiltonian does not possess this symmetry and consequently the
dynamics of the attractive and repulsive junctions are different.
