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This paper concerns the asymptotic ground state properties of heavy atoms instrong, homogeneous magnetic fields. In the limit when the nuclear charge Ztends to infinity with the magnetic field B satisfying B >> Z^{4/3} all theelectrons are confined to the lowest Landau band. We consider here an energyfunctional, whose variable is a sequence of one-dimensional density matricescorresponding to different angular momentum functions in the lowest Landauband. We study this functional in detail and derive various interestingproperties, which are compared with the density matrix (DM) theory introducedby Lieb, Solovej and Yngvason. In contrast to the DM theory the variableperpendicular to the field is replaced by the discrete angular momentum quantumnumbers. Hence we call the new functional a discrete density matrix (DDM)functional. We relate this DDM theory to the lowest Landau band quantummechanics and show that it reproduces correctly the ground state energy apartfrom errors due to the indirect part of the Coulomb interaction energy.Comment: LaTeX2e, 22 page

A Discrete Density Matrix Theory for Atoms¶in Strong Magnetic Fields