Localization for Schrödinger operators with Poisson random potential
Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 577-607
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We prove exponential and dynamical localization for the Schrödinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.
@article{JEMS_2007_9_3_a6,
author = {Fran\c{c}ois Germinet and Peter D. Hislop and Abel Klein},
title = {Localization for {Schr\"odinger} operators with {Poisson} random potential},
journal = {Journal of the European Mathematical Society},
pages = {577--607},
publisher = {mathdoc},
volume = {9},
number = {3},
year = {2007},
doi = {10.4171/jems/89},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/89/}
}
TY - JOUR AU - François Germinet AU - Peter D. Hislop AU - Abel Klein TI - Localization for Schrödinger operators with Poisson random potential JO - Journal of the European Mathematical Society PY - 2007 SP - 577 EP - 607 VL - 9 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/89/ DO - 10.4171/jems/89 ID - JEMS_2007_9_3_a6 ER -
%0 Journal Article %A François Germinet %A Peter D. Hislop %A Abel Klein %T Localization for Schrödinger operators with Poisson random potential %J Journal of the European Mathematical Society %D 2007 %P 577-607 %V 9 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4171/jems/89/ %R 10.4171/jems/89 %F JEMS_2007_9_3_a6
François Germinet; Peter D. Hislop; Abel Klein. Localization for Schrödinger operators with Poisson random potential. Journal of the European Mathematical Society, Tome 9 (2007) no. 3, pp. 577-607. doi: 10.4171/jems/89
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