[Localisation d'Anderson pour un système à deux particules, à basses énergies]
On démontre la localisation spectrale exponentielle pour un modèle d'Anderson discret, avec interaction à courte portée dans un champ de potentiel aléatoire i.i.d., à basses énergies. La démonstration utilise l'analyse multi-échelle multi-particule développée dans Chulaevsky et Suhov (2009) [4] dans le cas de grand désordre. Cette méthode s'applique à une classe de potentiels aléatoires plus large que dans Aizenman et Warzel (2009) [2], où la localisation dynamique a été démontrée par la méthode des moments fractionnaires.
We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and an external i.i.d. random potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale analysis developed earlier in Chulaevsky and Suhov (2009) [4] in the case of high disorder. Our method applies to a larger class of random potentials than in Aizenman and Warzel (2009) [2] where dynamical localization was proved with the help of the fractional moment method.
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@article{CRMATH_2011__349_3-4_167_0,
author = {Ekanga, Tr\'esor},
title = {On two-particle {Anderson} localization at low energies},
journal = {Comptes Rendus. Math\'ematique},
pages = {167--170},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2010.11.003},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.11.003/}
}
TY - JOUR AU - Ekanga, Trésor TI - On two-particle Anderson localization at low energies JO - Comptes Rendus. Mathématique PY - 2011 SP - 167 EP - 170 VL - 349 IS - 3-4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.11.003/ DO - 10.1016/j.crma.2010.11.003 LA - en ID - CRMATH_2011__349_3-4_167_0 ER -
%0 Journal Article %A Ekanga, Trésor %T On two-particle Anderson localization at low energies %J Comptes Rendus. Mathématique %D 2011 %P 167-170 %V 349 %N 3-4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.11.003/ %R 10.1016/j.crma.2010.11.003 %G en %F CRMATH_2011__349_3-4_167_0
Ekanga, Trésor. On two-particle Anderson localization at low energies. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 167-170. doi : 10.1016/j.crma.2010.11.003. http://archive.numdam.org/articles/10.1016/j.crma.2010.11.003/
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