Atoms with bosonic "electrons" in strong magnetic fields

B. Baumgartner, R. Seiringer, Annales Henri Poincare 2 (2001) 41–76.


Journal Article | Published
Author
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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→∞ with N / Z fixed, and identify three different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . 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≫Z3 ; i.e., for very strong magnetic fields the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general 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.
Publishing Year
Date Published
2001-02-01
Journal Title
Annales Henri Poincare
Volume
2
Issue
1
Page
41 - 76
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Cite this

Baumgartner B, Seiringer R. Atoms with bosonic "electrons" in strong magnetic fields. Annales Henri Poincare. 2001;2(1):41-76. doi:10.1007/PL00001032
Baumgartner, B., & Seiringer, R. (2001). Atoms with bosonic "electrons" in strong magnetic fields. Annales Henri Poincare, 2(1), 41–76. https://doi.org/10.1007/PL00001032
Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons" in Strong Magnetic Fields.” Annales Henri Poincare 2, no. 1 (2001): 41–76. https://doi.org/10.1007/PL00001032.
B. Baumgartner and R. Seiringer, “Atoms with bosonic "electrons" in strong magnetic fields,” Annales Henri Poincare, vol. 2, no. 1, pp. 41–76, 2001.
Baumgartner B, Seiringer R. 2001. Atoms with bosonic "electrons" in strong magnetic fields. Annales Henri Poincare. 2(1), 41–76.
Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons" in Strong Magnetic Fields.” Annales Henri Poincare, vol. 2, no. 1, Birkhäuser, 2001, pp. 41–76, doi:10.1007/PL00001032.

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