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Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors

A. Minguzzi·N. H. March·M. P. Tosi
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Abstract

We evaluate analytically some ground state properties of two-dimensional harmonically confined Fermi vapors with isotropy and for an arbitrary number of closed shells. We first derive a differential form of the virial theorem and an expression for the kinetic energy density in terms of the fermion particle density and its low-order derivatives. These results allow an explicit differential equation to be obtained for the particle density. The equation is third-order, linear and homogeneous. We also obtain a relation between the turning points of kinetic energy and particle densities, and an expression of the non-local kinetic energy density functional.

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A. Minguzzi, N. H. March, M. P. Tosi. 2001-02-10. Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors. https://doi.org/10.1007/s100530170146

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