Christian Hainzl, Robert Seiringer
A discrete density matrix theory for atoms in strong magnetic fields
(50K, LaTeX2e)
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 $\infty$ with the magnetic field $B$
satisfying $B \gg Z^{4/3}$ 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 {\it 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.