Eur. Phys. J. D 15, 315-320 (2001)
https://doi.org/10.1007/s100530170146

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

¹ Istituto Nazionale per la Fisica della Materia and Classe di Scienze, Scuola Normale Superiore, Pisa, Italy
² Oxford University, Oxford, UK
³ Department of Physics, University of Antwerp (RUCA), Antwerp, Belgium

Corresponding author: ^a tosim@bib.sns.it

Received: 27 March 2001
Revised: 12 June 2001
Published online: 15 September 2001

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.