Atoms with bosonic "electrons" in strong magnetic fields

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.

LaTeX2e, 37 pages

References in corpus (4)

• Atoms in strong magnetic fields: The high field limit at fixed nuclear charge
• On the maximal ionization of atoms in strong magnetic fields
• Density Matrix Functional Calculations for Matter in Strong Magnetic Fields: I. Atomic Properties
• One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields

Cited by in corpus (4)

• The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion
• Ground-state properties of artificial bosonic atoms, Bose interaction blockade and the single-atom pipette
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• On the ordering of energy levels in homogeneous magnetic fields