Francois Germinet, Abel Klein
Explicit finite volume criteria for localization in continuous 
 random media and applications
(509K, .ps)

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.