Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
Brack, Matthias ; van Zyl, Brandon P.
arXiv, 0010201 / Harvested from arXiv
Text on arXiv
We derive simple analytical expressions for the particle density $\rho(r)$ and the kinetic energy density $\tau(r)$ for a system of noninteracting fermions in a $d-$dimensional isotropic harmonic oscillator potential. We test the Thomas-Fermi (TF, or local-density) approximation for the functional relation $\tau[\rho]$ using the exact $\rho(r)$ and show that it locally reproduces the exact kinetic energy density $\tau(r)$, {\it including the shell oscillations,} surprisingly well everywhere except near the classical turning point. For the special case of two dimensions (2D), we obtain the unexpected analytical result that the integral of $\tau_{TF}[\rho(r)]$ yields the {\it exact} total kinetic energy.
Publié le : 2000-10-15
Classification:  Condensed Matter - Mesoscale and Nanoscale Physics,  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Physics - Classical Physics 
@article{0010201,
     author = {Brack, Matthias and van Zyl, Brandon P.},
     title = {Simple Analytical Particle and Kinetic Energy Densities for a Dilute
  Fermionic Gas in a d-Dimensional Harmonic Trap},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0010201}
}

Brack, Matthias; van Zyl, Brandon P. Simple Analytical Particle and Kinetic Energy Densities for a Dilute
  Fermionic Gas in a d-Dimensional Harmonic Trap. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0010201/