  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 infinity with the magnetic field B satisfying B >> 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 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.
