### Abstract

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z → ∞. In this and a companion work (see [28]) we show that there are five regions as Z → ∞: B < Z^{4/3}, B ∼ Z^{4/3}, Z^{4/3} < B < Z^{3}, B ∼ Z^{3}, B > Z^{3}. Regions 1, 2, 3, and 4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions 1, 2, and 3 are described by a simple density functional theory of the semiclassical Thomas‐Fermi form. Here we concentrate mainly on regions 4 and 5 which cannot be so described, although 3, 4, and 5 have the common feature (as shown here) that essentially all electrons are in the lowest Landau band. Region 5 does have, however, a simple non‐classical density functional theory (which can be solved exactly). Region 4 does not, but, surprisingly, it can be described by a novel density matrix functional theory. © 1994 John Wiley & Sons, Inc.

Original language | English (US) |
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Pages (from-to) | 513-591 |

Number of pages | 79 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1994 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Communications on Pure and Applied Mathematics*,

*47*(4), 513-591. https://doi.org/10.1002/cpa.3160470406