How correlation suppresses density fluctuations in the uniform electron gas of one, two, or three dimensions

The particle number N fluctuates in a spherical volume fragment Ω of a uniform electron gas. In an ideal classical-gas or “Hartree” model, the fluctuation is strong, with (ΔNΩ)2=NΩ. We show in detail how this fluctuation is reduced by exchange in the ideal Fermi gas and further reduced by Coulomb correlation in the interacting Fermi gas. Besides the mean particle number NΩ and mean square fluctuation (ΔNΩ)2=(N2)Ω−(NΩ)2, we also examine the full probability distribution PΩ(N). The latter is approximately Gaussian, and exactly Gaussian for \documentclass{article}\pagestyle{empty}\begin{document}$N_{\Omega}\gg1$\end{document}. More precisely, for any NΩ it is a Poisson distribution for the ideal classical gas and a modified Poisson distribution for the ideal or interacting Fermi gases. While most of our results are for nonzero densities and three dimensions, we also consider fluctuations in the low-density or strictly correlated limit and in the electron gas of one or two dimensions. In one dimension, the electrons may be strictly correlated at all finite densities. Fulde's fluctuation-based index of correlation strength applies to the uniform gas in any number of dimensions. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 819–830, 2000