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TheN 7/5 law for charged bosons

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Abstract

Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfiesE 0≦−AN 7/5. We prove that 7/5 is the correct power by proving thatE 0≧−BN 7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed thatE 0≦−CNρ1/4. This 1/4 law is also validated here by showing thatE 0≧−DNρ1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

    Joseph G. Conlon

  2. Departments of Mathematics and Physics, Princeton University, P.O.B. 708, 08544, Princeton, NJ, USA

    Elliott H. Lieb & Horng-Tzer Yau

Authors
  1. Joseph G. Conlon
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  2. Elliott H. Lieb
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  3. Horng-Tzer Yau
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Additional information

Communicated by A. Jaffe

Work partially supported by U.S. National Science Foundation grant DMS 8600748

Work partially supported by U.S. National Science Foundation grant PHY85-15288-A01

Work supported by Alfred Sloan Foundation dissertation fellowship

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Conlon, J.G., Lieb, E.H. & Yau, HT. TheN 7/5 law for charged bosons. Commun.Math. Phys. 116, 417–448 (1988). https://doi.org/10.1007/BF01229202

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