A discrete density matrix theory for atoms in strong magnetic fields

C. Hainzl, R. Seiringer, Communications in Mathematical Physics 217 (2001) 229–248.


Journal Article | Published
Author
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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
Volume
217
Issue
1
Page
229 - 248
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/s002200100373
Hainzl, C., & Seiringer, R. (2001). A discrete density matrix theory for atoms in strong magnetic fields. Communications in Mathematical Physics, 217(1), 229–248. https://doi.org/10.1007/s002200100373
Hainzl, Christian, and Robert Seiringer. “A Discrete Density Matrix Theory for Atoms in Strong Magnetic Fields.” Communications in Mathematical Physics 217, no. 1 (2001): 229–48. 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, pp. 229–248, 2001.
Hainzl C, Seiringer R. 2001. A discrete density matrix theory for atoms in strong magnetic fields. Communications in Mathematical Physics. 217(1), 229–248.
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.

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