## Abstract

We continue the study of the two-component charged Bose gas initiated by Dyson in 1967. He showed that the ground state energy for N particles is at least as negative as -CN^{7/5} for large N and this power law was verified by a lower bound found by Conlon, Lieb and Yau in 1988. Dyson conjectured that the exact constant C was given by a mean-field minimization problem that used, as input, Foldy's calculation (using Bogolubov's 1947 formalism) for the one-component gas. Earlier we showed that Foldy's calculation is exact insofar as a lower bound of his form was obtained. In this paper we do the same thing for Dyson's conjecture. The two-component case is considerably more difficult because the gas is very non-homogeneous in its ground state.

Original language | English (US) |
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Pages (from-to) | 485-534 |

Number of pages | 50 |

Journal | Communications In Mathematical Physics |

Volume | 252 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 2004 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics