To complement existing knowledge of the density matrix gamma(F)(x, y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix gamma(IB)(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 numericallyi Finally, the functional relationship between M(x. y) and yF(x, y) is formally set out and illustrated. (c) 2006 Elsevier B.V. All rights reserved.
First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps
2007
Abstract
To complement existing knowledge of the density matrix gamma(F)(x, y) of independent fermions for N particles in one dimension under harmonic confinement, the corresponding matrix gamma(IB)(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 numericallyi Finally, the functional relationship between M(x. y) and yF(x, y) is formally set out and illustrated. (c) 2006 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
