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Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions
Author(s) -
Lieb Elliott H.,
Solovej Jan Philip,
Yngvason Jakob
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470406
Subject(s) - semiclassical physics , physics , landau quantization , simple (philosophy) , magnetic field , electron , ground state , atom (system on chip) , density functional theory , quantum mechanics , density matrix , charge (physics) , order (exchange) , fermi gamma ray space telescope , mathematical physics , atomic physics , quantum , philosophy , epistemology , finance , computer science , economics , embedded system
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.