A discrete density matrix theory for atoms in strong magnetic fields Journal Article

Author(s): Hainzl, Christian; Seiringer, Robert
Article Title: A discrete density matrix theory for atoms in strong magnetic fields
Abstract: This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy.
Journal Title: Communications in Mathematical Physics
Volume: 217
Issue 1
ISSN: 1432-0916
Publisher: Springer  
Date Published: 2001-02-01
Start Page: 229
End Page: 248
DOI: 10.1007/s002200100373
Open access: yes (repository)
IST Austria Authors
  1. Robert Seiringer
    123 Seiringer
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