Elliott H. Lieb and Jan Philip Solovej
GROUND STATE ENERGY OF THE TWO-COMPONENT CHARGED BOSE GAS
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ABSTRACT. We continue the study of the two-component charged Bose gas
initiated by Dyson in 1967. He showed that the ground state energy
for $N$ particles is at least as negative as $-CN^{7/5}$ for large
$N$ and this power law was verified by a lower bound found by Conlon, Lieb and Yau in 1988. Dyson conjectured that the exact constant $C$ was given by a mean-field minimization problem that used, as input, Foldy's
calculation (using Bogolubov's 1947 formalism) for the one-component
gas. Earlier we showed that Foldy's calculation is exact insofar as
a lower bound of his form was obtained. In this paper we do the same
thing for Dyson's conjecture. The two-component case is considerably
more difficult because the gas is very non-homogeneous in its ground
state.