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Explicit finite volume criteria for localization in continuous random media and applications

Authors: Germinet, François; Klein, A.;

Explicit finite volume criteria for localization in continuous random media and applications

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 \(C_\lambda\) for large \(\lambda\), where \(\lambda\) 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 \[ C \frac{\log B}{B} \] from the Landau levels for large \(B\), where \(B\) is the strength of the magnetic field.

Country
France
Keywords

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, Random linear operators, Applications of operator theory in statistical physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
34
Top 10%
Top 10%
Top 10%
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