Hard-core bosons and spinless fermions trapped on 1D lattices

We study ground state properties and the non-equilibrium dynamics of trapped hard-core bosons on 1D lattices. We follow an exact approach based on the Jordan-Wigner transformation, which maps the hard-core boson Hamiltonian into the one of non-interacting spinless fermions. Off-diagonal one-particle correlations and the momentum distribution function of hard-core bosons and spinless fermions are contrasted in and out of equilibrium.