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Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 485–534 | Cite as

Ground State Energy of the Two-Component Charged Bose Gas

  • Elliott H. Lieb
  • Jan Philip SolovejEmail author
Article

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 −CN7/5 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© E.H. Lieb and J.P. Solovej 2004

Authors and Affiliations

  1. 1.Departments of Physics and MathematicsJadwin Hall, Princeton UniversityPrincetonUSA
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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