Exact particle and kinetic energy densities for one-dimensional confined   gases of non-interacting fermions
  We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting 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 (local density) approximation, the exact profiles under harmonic confinement 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. 
Patrizia Vignolo, Anna Minguzzi and M. P. Tosi (SNS, Pisa)