# A discrete density matrix theory for atoms in strong magnetic fields

Hainzl C, Seiringer R. 2001. A discrete density matrix theory for atoms in strong magnetic fields. Communications in Mathematical Physics. 217(1), 229–248.

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http://arxiv.org/abs/math-ph/0010005
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*Journal Article*|

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*English*

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Author

Hainzl, Christian;
Seiringer, Robert

^{ISTA}^{}Abstract

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B ≫ Z4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy.

Publishing Year

Date Published

2001-02-01

Journal Title

Communications in Mathematical Physics

Acknowledgement

The authors would like to thank Bernhard Baumgartner and Jakob Yngvason for proofreading and valuable comments.

Volume

217

Issue

1

Page

229 - 248

ISSN

IST-REx-ID

### Cite this

Hainzl C, Seiringer R. A discrete density matrix theory for atoms in strong magnetic fields.

*Communications in Mathematical Physics*. 2001;217(1):229-248. doi:10.1007/s002200100373Hainzl, C., & Seiringer, R. (2001). A discrete density matrix theory for atoms in strong magnetic fields.

*Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s002200100373Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory for Atoms in Strong Magnetic Fields.”

*Communications in Mathematical Physics*. Springer, 2001. https://doi.org/10.1007/s002200100373.C. Hainzl and R. Seiringer, “A discrete density matrix theory for atoms in strong magnetic fields,”

*Communications in Mathematical Physics*, vol. 217, no. 1. Springer, pp. 229–248, 2001.Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory for Atoms in Strong Magnetic Fields.”

*Communications in Mathematical Physics*, vol. 217, no. 1, Springer, 2001, pp. 229–48, doi:10.1007/s002200100373.**All files available under the following license(s):**

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arXiv math-ph/0010005