The N7/5 law for charged bosons

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

doi:10.1007/BF01229202

The N^7/5 law for charged bosons

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

Mathematics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

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

Original language	English (US)
Pages (from-to)	417-448
Number of pages	32
Journal	Communications In Mathematical Physics
Volume	116
Issue number	3
DOIs	https://doi.org/10.1007/BF01229202
State	Published - Sep 1988

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01229202

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title = "The N7/5 law for charged bosons",

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.",

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AU - Lieb, Elliott H.

AU - Yau, Horng Tzer

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N2 - 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.

AB - 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.

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The N^7/5 law for charged bosons

Abstract

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