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Communications in Theoretical Physics

Simple Method Obtaining Analytical Expressions of Particle and Kinetic-Energy Densities for One-Dimensional Confined Fermi Gases

Xiaoxue Yang, Ying Wu

Published Mar 15, 2002• 0 citations
Publisher

Abstract

We develop a simple approach to obtain explicitly exact analytical expressions of particle and kinetic-energy densities for noninteracting Fermi gases in one-dimensional harmonic confinement, and in one-dimensional box confinement as well.
DOI
10.1088/0253-6102/37/3/293

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We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of noninteracting fermions, and apply it to harmonically confined systems of up to N = 1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact profiles show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.
Using the known perturbation series for the idempotent Dirac density matrix in powers of a given one-body potential V(r)V(\mathbf{r})V(r), Stoddart and March (SM) generated a corresponding series for the kinetic energy density. While the general term of the SM series is known, a summation has not been achieved to date. A contribution to solve this problem is made here by exhibiting an explicit form of the above kinetic energy density for Fermions filling an arbitrary number of closed shells, when the confinement is harmonic. This example is of considerable current interest because of ongoing experiments on ultracold atomic gases of Fermions.