 00283 Bernhard Baumgartner, Robert Seiringer
 Atoms with bosonic ``electrons'' in strong magnetic fields
(91K, LaTeX2e)
Jul 5, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

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 onedimensional functional, which is
identical to the socalled HyperStrong
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 oneparticle 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.
 Files:
00283.src(
00283.keywords ,
baum_seir.tex )