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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-31
August 2000

Ground state energy of the one-component charged Bose gas


Jan Philip Solovej

Elliott H. Lieb


The model considered here is the `jellium' model in which there is a uniform, fixed background with charge density $-e\rho$ in a large volume $V$ and in which $N=\rho V$ particles of electric charge $+e$ and mass $m$ move --- the whole system being neutral. In 1961 Foldy used Bogolubov's 1947 method to investigate the ground state energy of this system for bosonic particles in the large $\rho$ limit. He found that the energy per particle is $-0.402 \, r_s^{-3/4} {me^4}/{\hbar^2}$ in this limit, where $r_s=(3/4\pi \rho)^{1/3}e^2m/\hbar^2$. Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov's pairing theory of the Bose gas.

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This paper has now been published in Commun. Math. Phys. 217. Issue 1 (2001) pp. 127-163.