The N7/5 Law for Charged Bosons

  • Joseph G. Conlon
  • Elliott H. Lieb
  • Horng-Tzer Yau


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


Kinetic Energy Thermodynamic Limit Coulomb Potential Yukawa Potential Neutral Case 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Joseph G. Conlon
    • 1
  • Elliott H. Lieb
    • 2
  • Horng-Tzer Yau
    • 2
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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