Explicit finite volume criteria for localization in continuous random media and applications |
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Authors: | Email author" target="_blank">Fran?ois?GerminetEmail author Abel?Klein |
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Institution: | (1) UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d Ascq Cédex, France;(2) Present address: Departement de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France;(3) Department of Mathematics, University of California at Irvine, Irvine, 92697-3875, CA, USA |
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Abstract: | We give finite volume criteria for localization of quantum or classical
waves in continuous random media. We provide explicit conditions,
depending on the parameters of the model, for starting the bootstrap
multiscale analysis. A simple application to Anderson Hamiltonians
on the continuum yields localization at the bottom of the spectrum
in an interval of size C for large , where stands for the disorder
parameter. A more sophisticated application proves localization for
two-dimensional random Schrödinger operators in a constant magnetic
field (random Landau Hamiltonians) up to a distance
from the Landau levels for large B, where B is the strength of the
magnetic field. |
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Keywords: | ((no )) |
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