On localization for the Schrödinger operator with a Poisson random potential

François Germinet; Peter Hislop; Abel Klein

doi:10.1016/j.crma.2005.09.001

On localization for the Schrödinger operator with a Poisson random potential

François Germinet, Peter Hislop, Abel Klein

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	525-528
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	341
Issue number	8
DOIs	https://doi.org/10.1016/j.crma.2005.09.001
State	Published - Oct 15 2005

Bibliographical note

Funding Information:
E-mail addresses: germinet@math.u-cergy.fr (F. Germinet), hislop@ms.uky.edu (P. Hislop), aklein@math.uci.edu (A. Klein). 1 Currently visiting the Université de Paris Nord with support from the CNRS. 2 Partially supported by NSF Grant DMS-0202656. 3 Partially supported by NSF Grant DMS-0200710.

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.crma.2005.09.001

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title = "On localization for the Schr{\"o}dinger operator with a Poisson random potential",

abstract = "We prove exponential localization for the Schr{\"o}dinger 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.",

author = "Fran{\c c}ois Germinet and Peter Hislop and Abel Klein",

note = "Funding Information: E-mail addresses: germinet@math.u-cergy.fr (F. Germinet), hislop@ms.uky.edu (P. Hislop), aklein@math.uci.edu (A. Klein). 1 Currently visiting the Universit{\'e} de Paris Nord with support from the CNRS. 2 Partially supported by NSF Grant DMS-0202656. 3 Partially supported by NSF Grant DMS-0200710.",

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T1 - On localization for the Schrödinger operator with a Poisson random potential

AU - Germinet, François

AU - Hislop, Peter

AU - Klein, Abel

N1 - Funding Information: E-mail addresses: germinet@math.u-cergy.fr (F. Germinet), hislop@ms.uky.edu (P. Hislop), aklein@math.uci.edu (A. Klein). 1 Currently visiting the Université de Paris Nord with support from the CNRS. 2 Partially supported by NSF Grant DMS-0202656. 3 Partially supported by NSF Grant DMS-0200710.

PY - 2005/10/15

Y1 - 2005/10/15

N2 - 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.

AB - 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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IS - 8

ER -

On localization for the Schrödinger operator with a Poisson random potential

Abstract

Bibliographical note

ASJC Scopus subject areas

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