[Sur localization pour l'opérateur de Schrödinger avec un potentiel aléatoire de Poisson]
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.
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@article{CRMATH_2005__341_8_525_0,
author = {Germinet, Fran\c{c}ois and Hislop, Peter and Klein, Abel},
title = {On localization for the {Schr\"odinger} operator with a {Poisson} random potential},
journal = {Comptes Rendus. Math\'ematique},
pages = {525--528},
publisher = {Elsevier},
volume = {341},
number = {8},
year = {2005},
doi = {10.1016/j.crma.2005.09.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.09.001/}
}
TY - JOUR AU - Germinet, François AU - Hislop, Peter AU - Klein, Abel TI - On localization for the Schrödinger operator with a Poisson random potential JO - Comptes Rendus. Mathématique PY - 2005 SP - 525 EP - 528 VL - 341 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.09.001/ DO - 10.1016/j.crma.2005.09.001 LA - en ID - CRMATH_2005__341_8_525_0 ER -
%0 Journal Article %A Germinet, François %A Hislop, Peter %A Klein, Abel %T On localization for the Schrödinger operator with a Poisson random potential %J Comptes Rendus. Mathématique %D 2005 %P 525-528 %V 341 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.09.001/ %R 10.1016/j.crma.2005.09.001 %G en %F CRMATH_2005__341_8_525_0
Germinet, François; Hislop, Peter; Klein, Abel. On localization for the Schrödinger operator with a Poisson random potential. Comptes Rendus. Mathématique, Tome 341 (2005) no. 8, pp. 525-528. doi : 10.1016/j.crma.2005.09.001. http://www.numdam.org/articles/10.1016/j.crma.2005.09.001/
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