Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions

Elliott H. Lieb, Jan Philip Solovej, Jakob Yngvason

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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 < Z4/3, B ∼ Z4/3, Z4/3 < B < Z3, B ∼ Z3, B > Z3. 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 languageEnglish (US)
Pages (from-to)513-591
Number of pages79
JournalCommunications on Pure and Applied Mathematics
Volume47
Issue number4
DOIs
StatePublished - Apr 1994

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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