Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap

The exact N-particle ground-state wave function for a one-dimensional condensate of hard-core bosons in a harmonic trap is employed to obtain accurate numerical results for the one-particle density matrix, occupation number distribution of the natural orbitals, and momentum distribution. Our results show that the occupation of the lowest orbital varies as $N^{0.59},$ in contrast to $N^{0.5}$ for a spatially uniform system, and N for a true Bose-Einstein condensate.