### Abstract

The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and it is shown that grows monotonically in N > 1, where. The Newton systems are "bosonic stars," and it is shown that when the Bosons are centrally attracted to a fixed gravitational "grain" of mass M > 0, and N >2, then grows monotonically in N, where P_{N}(N) = N (N - 1)(N-2); in the translation-invariant problem (M = 0), it is shown that when N > 1 then grows monotonically in N, with from the Coulomb problem. Some applications of the new monotonicity results are discussed.

Original language | English (US) |
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Pages (from-to) | 1063-1078 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 137 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 2009 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Bosonic atoms
- Bosonic stars
- Ground state energies
- N body problems
- Non-relativistic quantum mechanics
- Rigorous results