  We study the ground-state properties of hard-core bosons trapped by arbitrary
confining potentials on one-dimensional optical lattices. A recently developed
exact approach based on the Jordan-Wigner transformation is used. We analyze
the large distance behavior of the one-particle density matrix, the momentum
distribution function, and the lowest natural orbitals. In addition, the
low-density limit in the lattice is studied systematically, and the results
obtained compared with the ones known for the hard-core boson gas without the
lattice.
