02-375 Francois Germinet, Abel Klein

Explicit finite volume criteria for localization in continuous random media and applications (509K, .ps) Sep 12, 02

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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 yields localization for Anderson Hamiltonians on the continuum at the bottom of the spectrum in an interval of size ${\mathcal{O}}({\lambda})$ for large ${\lambda}$, where ${\lambda}$ stands for the disorder parameter. A more sophisticated application proves localization for two-dimensional random Schr\"odinger operators in a constant magnetic field (random Landau Hamiltonians) up to a distance ${\mathcal{O}}(\frac{\log B}{B})$ from the Landau levels, where $B$ is the strength of the magnetic field.

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