Ground State Energy of the Two-Component Charged Bose Gas

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 $-C{N}^{7/5}$ 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.

arXiv comment49 pages, Dedicated to Freeman J. Dyson on the occasion of his 80th birthday. Final version (only minor changes) to appear in Commun. math. Phys

References in corpus (2)

• Ground State Energy of the One-Component Charged Bose Gas
• Upper Bounds to the Ground State Energies of the One- and Two-Component Charged Bose Gases

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