Bernhard Baumgartner, Robert Seiringer
Atoms with bosonic ``electrons'' in strong magnetic fields
(91K, LaTeX2e)

ABSTRACT.  We study the ground state properties of an atom with nuclear 
charge $Z$ and $N$ bosonic ``electrons'' in the presence 
of a homogeneous magnetic field $B$. We investigate the mean field 
limit $N\to\infty$ with $N/Z$ fixed, and identify three different 
asymptotic regions, according to $B\ll Z^2$, $B\sim Z^2$, and 
$B\gg Z^2$. In Region 1 standard Hartree theory is applicable. 
Region 3 is described by a one-dimensional functional, which is 
identical to the so-called Hyper-Strong 
functional introduced by Lieb, Solovej and Yngvason 
for atoms with fermionic electrons in the 
region $B\gg Z^3$; i.e., for very strong magnetic fields the ground state 
properties of atoms are independent of statistics. For Region 2 
we introduce a general {\it magnetic 
Hartree functional}, which is studied in detail. It is shown that 
in the special case of an atom it can be restricted to the subspace of zero 
angular momentum parallel to the magnetic field, which simplifies 
the theory considerably. The functional reproduces the energy and 
the one-particle reduced density matrix for the full $N$-particle 
ground state to leading order in $N$, and it implies the 
description of the other regions as limiting cases.