Density profile of a harmonically trapped ideal Fermi gas in arbitrary dimension

Abstract

Closed form analytic expressions are derived for the density profile of a harmonically trapped noninteracting Fermi gas in $d$ dimensions. Shell structure effects are included to leading order in 1/N, where $N$ is the number of particles. These corrections to the local density approximation scale as $\delta n/n\sim N^{-\alpha }$, where $\alpha =(1+1/d)/2$.

arXiv comment4 pages, 1 color figure, 2 bw figures, RevTeX4 -- updated reference

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• Thermodynamics of low-dimensional trapped Fermi gases
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• Exact and asymptotic local virial theorems for finite fermionic systems
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