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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 −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.

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Authors and Affiliations

  1. Departments of Physics and Mathematics, Jadwin Hall, Princeton University, 708, Princeton, NJ, 08544-0708, USA

    Elliott H. Lieb

  2. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540, USA

    Jan Philip Solovej

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  1. Elliott H. Lieb
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  2. Jan Philip Solovej
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Correspondence to Jan Philip Solovej.

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Communicated by M. Aizenman

Dedicated to Freeman J. Dyson on the occasion of his 80th birthday

©2003 by the authors. This article may be reproduced in its entirety for non-commercial purposes.

Work partially supported by NSF grant DMS-0111298, by EU grant HPRN-CT-2002-00277, by MaPhySto – A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation, and by grants from the Danish research council.

Work partially supported by U.S. National Science Foundation grant PHY01 39984-A01.

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Lieb, E., Solovej, J. Ground State Energy of the Two-Component Charged Bose Gas. Commun. Math. Phys. 252, 485–534 (2004). https://doi.org/10.1007/s00220-004-1144-1

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