Brack, M. ; Murthy, M. V. N. (2003) Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions Journal of Physics A: Mathematical and General, 36 (4). pp. 1111-1134. ISSN 1751-8113
Full text not available from this repository.
Official URL: http://iopscience.iop.org/0305-4470/36/4/318
Related URL: http://dx.doi.org/10.1088/0305-4470/36/4/318
Abstract
We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive differential equations connecting these densities, which so far have been proved only in one or two dimensions, and give other interesting relations involving several densities or the particle density alone. We show that in the asymptotic limit of large particle numbers, the densities go over into the semi-classical Thomas-Fermi (TF) densities. Hereby the Fermi energy to be used in the TF densities is uniquely identified. We derive an analytical expansion for the remaining oscillating parts and obtain very simple closed forms for the leading-order oscillating densities. Finally, we show that the simple TF functional relation ΤTF[ρ] between kinetic and particle densities is also fulfilled for the asymptotic quantum densities Τ(r) and ρ(r) including their leading-order oscillating terms.
Item Type: | Article |
---|---|
Source: | Copyright of this article belongs to Institute of Physics. |
ID Code: | 79629 |
Deposited On: | 27 Jan 2012 11:39 |
Last Modified: | 27 Jan 2012 11:39 |
Repository Staff Only: item control page