Ground state energy of the two-component charged Bose gas

Elliott Lieb, Jan Philip Solovej

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages849-898
Number of pages50
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - Jan 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Lieb, E., & Solovej, J. P. (2005). Ground state energy of the two-component charged Bose gas. In The Stability of Matter: From Atoms to Stars: Fourth Edition (pp. 849-898). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_51