Author(s):

Hainzl, Christian; Seiringer, Robert

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

Affiliation 

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 onedimensional 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:

14320916

Publisher:

Springer

Date Published:

20010201

Start Page: 
229

End Page:

248

URL: 

DOI: 
10.1007/s002200100373

Open access: 
yes (repository) 