Ground State Energy of the Two-Component Charged Bose Gas

Details Ground State Energy of the Two-Component Charged Bose Gas Ground State Energy of the Two-Component Charged Bose Gas

2003-11-07

arxiv.org/abs/math-ph/0311010v3

Physics

Mathematical Physics

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

Scientific paper

10.1007/s00220-004-1144-1

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.

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