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Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions

Patrizia Vignolo·Anna Minguzzi·M. P. Tosi
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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.

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Patrizia Vignolo, Anna Minguzzi, M. P. Tosi. 2000-09-06. Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions. https://doi.org/10.1103/physrevlett.85.2850

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