Localization for Schrödinger operators with Poisson random potential

Abel Klein; Peter Hislop; François Germinet

Journal of the European Mathematical Society (2007)

  • Volume: 009, Issue: 3, page 577-607
  • ISSN: 1435-9855

Abstract

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We prove exponential and dynamical localization for the Schr¨odinger 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.

How to cite

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Klein, Abel, Hislop, Peter, and Germinet, François. "Localization for Schrödinger operators with Poisson random potential." Journal of the European Mathematical Society 009.3 (2007): 577-607. <http://eudml.org/doc/277406>.

@article{Klein2007,
abstract = {We prove exponential and dynamical localization for the Schr¨odinger 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.},
author = {Klein, Abel, Hislop, Peter, Germinet, François},
journal = {Journal of the European Mathematical Society},
keywords = {Poisson random potential; random Schrödinger operator; eigenvalue; Wegner estimate; Poisson random potential; random Schrödinger operator; eigenvalue; Wegner estimate},
language = {eng},
number = {3},
pages = {577-607},
publisher = {European Mathematical Society Publishing House},
title = {Localization for Schrödinger operators with Poisson random potential},
url = {http://eudml.org/doc/277406},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Klein, Abel
AU - Hislop, Peter
AU - Germinet, François
TI - Localization for Schrödinger operators with Poisson random potential
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 3
SP - 577
EP - 607
AB - We prove exponential and dynamical localization for the Schr¨odinger 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.
LA - eng
KW - Poisson random potential; random Schrödinger operator; eigenvalue; Wegner estimate; Poisson random potential; random Schrödinger operator; eigenvalue; Wegner estimate
UR - http://eudml.org/doc/277406
ER -

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