Comptes Rendus
no. 8
Mathematical Physics/Partial Differential Equations
On localization for the Schrödinger operator with a Poisson random potential
[Sur localization pour l'opérateur de Schrödinger avec un potentiel aléatoire de Poisson]

Présenté par : Jean-Michel Bony

François Germinet1 ; Peter Hislop2 ; Abel Klein3
1 Département de mathématiques, université de Cergy-Pontoise, 2, avenue A. Chauvin, 95302 Cergy-Pontoise cedex, France
2 Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA
3 University of California, Irvine, Department of Mathematics, Irvine, CA 92697-3875, USA
Comptes Rendus. Mathématique, Volume 341 (2005) no. 8, pp. 525-528.

On démontre localization exponentielle pour l'opérateur de Schrödinger avec un potentiel aléatoire de Poisson, pour les basses energies et en toute dimension. On démontre aussi localization exponentielle dans un intervalle d'énergies donné et à grande densité. On obtient de plus localisation dynamique et le fait que la multiplicité des valeurs propres est finie.

We prove exponential localization for the Schrödinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson densities. In addition, we obtain dynamical localization and finite multiplicity of the eigenvalues.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.09.001
François Germinet 1 ; Peter Hislop 2 ; Abel Klein 3

1 Département de mathématiques, université de Cergy-Pontoise, 2, avenue A. Chauvin, 95302 Cergy-Pontoise cedex, France
2 Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA
3 University of California, Irvine, Department of Mathematics, Irvine, CA 92697-3875, USA 
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François Germinet; Peter Hislop; Abel Klein. On localization for the Schrödinger operator with a Poisson random potential. Comptes Rendus. Mathématique, Volume 341 (2005) no. 8, pp. 525-528. doi : 10.1016/j.crma.2005.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.001/

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