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Comptes Rendus Mathématique
Volume 343, n° 1
pages 27-30 (juillet 2006)
Doi : 10.1016/j.crma.2006.05.008
Received : 30 January 2006 ;  accepted : 15 May 2006
Lʼion hydrogénoïde piégé en électrodynamique quantique non relativiste
The confined hydrogenoïd ion in non-relativistic quantum electrodynamics
 

Laurent Amour , Jérémy Faupin
Laboratoire de mathématiques, UMR - CNRS 6056, université de Reims, Moulin de la Housse, BP 1039, 51687 Reims cedex 2, France 

Résumé

Nous considérons un noyau et un électron non relativistes interagissant avec un champ électromagnétique quantifié. Nous ne supposons pas le noyau fixe, mais nous supposons que le système est confiné par son centre de masse. Ce modèle est utilisé en physique théorique pour décrire lʼeffet Lamb-Dicke et lʼeffet Mössbauer. Nous définissons lʼhamiltonien associé au système en introduisant une troncature ultraviolette, puis nous prouvons lʼexistence dʼun état fondamental non dégénéré. Ce résultat est obtenu sans condition sur les constantes de couplage. Pour citer cet article : L. Amour, J. Faupin, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Abstract

We consider a system of a nucleus with an electron together with the quantized electromagnetic field. Instead of fixing the nucleus, the system is confined by its center of mass. This model is used in theoretical physics to explain the Lamb-Dicke and the Mössbauer effects. When an ultraviolet cut-off is imposed we initiate the spectral analysis of the Hamiltonian describing the system and we derive the existence of a ground state. This is achieved without conditions on the fine structure constant. To cite this article: L. Amour, J. Faupin, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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