Journal of the European Mathematical Society
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Localization for Schrödinger operators with Poisson random potential
François Germinet (1), Peter D. Hislop (2) and 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, KY 40506-0027, LEXINGTON, UNITED STATES
(3) Department of Mathematics, University of California, Irvine, CA 92697-3875, IRVINE, UNITED STATES
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.
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