92-103 Lieb E.H., Solovej , J.P., Yngvason , J.
ASYMPTOTICS OF HEAVY ATOMS IN HIGH MAGNETIC FIELDS: I. LOWEST LANDAU BAND REGIONS (209K, Plain TeX) Sep 1, 92
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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 $Z\to\infty$. In this and a companion work [28] we show that there are 5 regions as $Z\to\infty$: $B\ll Z^{4/3}$, $B\sim Z^{4/3}$, $Z^{4/3}\ll B\ll Z^3$, $B\sim Z^3$, $B\gg Z^3$. Regions 1,2,3,4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions 1,2,3 are described by a simple density functional theory of the semiclassical Thomas-Fermi form. Here we concentrate mainly on regions 4,5 which cannot be so described, although 3,4,5 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 {\it matrix } functional theory!

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