 03490 Elliott H. Lieb and Jan Philip Solovej
 GROUND STATE ENERGY OF THE TWOCOMPONENT CHARGED BOSE GAS
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Nov 7, 03

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Abstract. We continue the study of the twocomponent 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 meanfield minimization problem that used, as input, Foldy's
calculation (using Bogolubov's 1947 formalism) for the onecomponent
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 twocomponent case is considerably
more difficult because the gas is very nonhomogeneous in its ground
state.
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