First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF (x, y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix γIB (x, y) for impenetrable bosons is given for N = 2 and 3 (with the N = 4 form available also). For fermions the momentum density is then obtained and illustrated numerically for N = 10. The boson momentum density is studied analytically at high momentum p, the coefficients of the p-4 and p-6 terms being tabulated for N = 2 - 5 inclusive. Their dependence on powers of N is exhibited numerically. Finally, the functional relationship between γIB (x, y) and γF (x, y) is formally set out and illustrated. © 2006 Elsevier B.V. All rights reserved. Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Scuola Normale Superiore; Italia Fil: Howard, I. A.. Universiteit Antwerp; Bélgica Fil: March, N. H.. Universiteit Antwerp; Bélgica. University of Oxford; Reino Unido Fil: Tosi, M. P.. Scuola Normale Superiore; Italia