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

P. CAPUZZI; I. A. HOWARD; N. H. MARCH; M. P. TOSI

PHYSICS LETTERS A

Año: 2007 vol. 361 p. 261 - 264

0375-9601

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.