The N7/5 law for charged bosons

Joseph G. Conlon, Elliott H. Lieb, Horng Tzer Yau

Research output: Contribution to journalArticle

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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 satisfies E0≦-AN7/5. We prove that 7/5 is the correct power by proving that E0≧-BN7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed that E0≦-CNρ1/4. This 1/4 law is also validated here by showing that E0≧-DNρ1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.

Original languageEnglish (US)
Pages (from-to)417-448
Number of pages32
JournalCommunications in Mathematical Physics
Volume116
Issue number3
DOIs
StatePublished - Sep 1 1988

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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    Conlon, J. G., Lieb, E. H., & Yau, H. T. (1988). The N7/5 law for charged bosons. Communications in Mathematical Physics, 116(3), 417-448. https://doi.org/10.1007/BF01229202