# 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.

## Keywords

Neural Network Statistical Physic Complex System State Energy Nonlinear Dynamics## Preview

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## References

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