Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
arXiv:cond-mat/0009076 · doi:10.1103/PhysRevLett.85.2850
Abstract
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.
8 pages, 3 figures, accepted for publication in Phys. Rev. Lett
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