Abstract
The model considered here is the “jellium” model in which there is a uniform, fixed background with charge density -eρ in a large volume V and in which N = ρV particles of electric charge +e and mass m move — the whole system being neutral. In 1961 Foldy used Bogolubov’s 1947 method to investigate the ground state energy of this system for bosonic particles in the large p limit. He found that the energy per particle is -0.402r s -3/4 me 4/h 2 in this limit, where r s = (3/πρ)1/3 e 2 m/h 2. Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov’s pairing theory of the Bose gas.
Dedicated to Leslie L. Foldy on the occasion of his 80th birthday
© 2000 by the authors. This article may be reproduced in its entirety for non-commercial purposes.
Work partially supported by U.S. National Science Foundation grant PHY98 20650-A01.
Work partially supported by EU TMR grant, by the Danish Research Foundation Center MaPhySto, and by a grant from the Danish Research Council.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-662-04360-8_55
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bogolubov, N.N.: J. Phys. (U.S.S.R.) 11, 23 (1947);
Bogolubov, N.N. and Zubarev, D.N.: Sov. Phys. JETP 1, 83 (1955)
Conlon, J.G., Lieb, E.H. and Yau, H-T.: The N 7/5 law for charged bosons. Commun. Math. Phys. 116, 417–448 (1988)
Dyson, F.J.: Ground-state energy of a finite system of charged particles. J. Math. Phys. 8, 1538–1545 (1967)
Foldy, L.L.: Charged boson gas. Phys. Rev. 124, 649–651 (1961); Errata. ibid 125, 2208 (1962)
Girardeau, M.: Ground state of the charged Bose gas. Phys. Rev. 127, 1809–1818 (1962)
Girardeau, M. and Arnowitt, R.: Theory of many-boson systems: Pair theory. Phys.Rev. 113, 755–761 (1959)
Graf, G.M. : Stability of matter through an electrostatic inequality. Helv. Phys. Acta 70, 72–79 (1997)
Kennedy, T, Lieb, E.H. and Shastry, S.: The XY model has long-range order for all spins and all dimensions greater than one. Phys. Rev. Lett. 61, 2582–2585 (1988)
Lieb, E.H.: The Bose fluid. In: Lecture Notes in Theoretical Physics VIIC, edited by W.E. Brittin. Univ. of Colorado Press, 1964, pp. 175–224
Lieb, E.H. and Sakakura, A. Y: Simplified approach to the ground state energy of an imperfect Bose gas II. Charged Bose gas at high density. Phys. Rev. A 133, 899–906 (1964)
Lieb, E.H. and Lebowitz, J.L.: The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Adv. in Math. 9, 316–398 (1972)
Lieb, E.H. and Liniger, W.: Exact analysis of an interacting Bose gas I. The general solution and the ground state. Phys. Rev. 130, 1605–1616 (1963). See Fig. 3
Lieb, E.H. and Narnhofer, H.: The thermodynamic limit for jellium. J. Stat. Phys. 12, 295–310 (1975); Errata. 14, 465 (1976)
Lieb, E.H. and Yngvason, J.: Ground state energy of the low density Bose gas. Phys. Rev. Lett. 80, 2504–2507(1998)
Elliott, H. Liev and Jan Philip Solovej, Ground State Energy of the One-Component Charged Bose Gas, Commun. Math. Phys. 217, 217–163 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lieb, E.H., Solovej, J.P. (2001). Ground State Energy of the One-Component Charged Bose Gas. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_49
Download citation
DOI: https://doi.org/10.1007/978-3-662-04360-8_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-04362-2
Online ISBN: 978-3-662-04360-8
eBook Packages: Springer Book Archive