Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2003-06-12
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
12 pages, 3 figures included in the text, RevTeX4. Text before Eq.(25) corrected. Additional equation following Eq.(25) has be
Scientific paper
10.1103/PhysRevA.68.033601
We present an exact closed form expression for the {\em finite temperature} first-order density matrix of a harmonically trapped ideal Fermi gas in any dimension. This constitutes a much sought after generalization of the recent results in the literature, where exact expressions have been limited to quantities derived from the {\em diagonal} first-order density matrix. We compare our exact results with the Thomas-Fermi approximation (TFA) and demonstrate numerically that the TFA provides an excellent description of the first-order density matrix in the large-N limit. As an interesting application, we derive a closed form expression for the finite temperature Hartree-Fock exchange energy of a two-dimensional parabolically confined quantum dot. We numerically test this exact result against the 2D TF exchange functional, and comment on the applicability of the local-density approximation (LDA) to the exchange energy of an inhomogeneous 2D Fermi gas.
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