P. Vignolo et al., Exact particle and kinetic-energy densities for one-dimensional confined gases of noninteracting fermions, PHYS REV L, 85(14), 2000, pp. 2850-2853
We propose a new method for the evaluation of the particle density and kine
tic pressure profiles in inhomogeneous one-dimensional systems of nonintera
cting 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 calcula
tion of the density of single-particle states from Green's functions in the
energy domain. In contrast to the Thomas-Fermi approximation, the exact pr
ofiles show negative local pressure in the tails and a prominent shell stru
cture which may become accessible to observation in magnetically trapped ga
ses of fermionic alkali atoms.