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Effective Hamiltonians for atoms in very strong magnetic fields

Effective Hamiltonians for atoms in very strong magnetic fields

Authors :
Raymond Brummelhuis
Pierre Duclos
Bernardo, Elizabeth
Laboratoire de Mathématiques de Reims (LMR)
Université de Reims Champagne-Ardenne (URCA)-Centre National de la Recherche Scientifique (CNRS)
Centre de Physique Théorique - UMR 6207 (CPT)
Centre National de la Recherche Scientifique (CNRS)-Université de Toulon (UTLN)-Université de Provence - Aix-Marseille 1-Université de la Méditerranée - Aix-Marseille 2
Centre de Physique Théorique - UMR 7332 (CPT)
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Source :
Journal of Mathematical Physics, Journal of Mathematical Physics, American Institute of Physics (AIP), 2006, 47, Journal of Mathematical Physics, 2006, 47
Publication Year :
2006
Publisher :
HAL CCSD, 2006.

Abstract

We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians describe $N$ electrons and a fixed nucleus where the Coulomb interaction has been replaced by $B$-dependent one-dimensional effective (vector valued) potentials but without magnetic field. Two of them are solvable in at least the one electron case. We briefly sketch how these Hamiltonians can be used to analyse the bottom of the spectrum of such atoms.<br />43 pages

Details

Language :
English
ISSN :
00222488
Database :
OpenAIRE
Journal :
Journal of Mathematical Physics, Journal of Mathematical Physics, American Institute of Physics (AIP), 2006, 47, Journal of Mathematical Physics, 2006, 47
Accession number :
edsair.doi.dedup.....c808c60b4ed5ba479c9f81340b5a3f8e