2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23448Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation $λ_η$ of the natural orbitals for large-$η$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.Revtex file, 5 pages, 5 figures. Content and references added. Published versionStatistical Mechanicstext