Anne Boutet de Monvel, Peter Stollmann, G\"unter Stolz
Absence of continuous spectral types for certain nonstationary random models
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ABSTRACT.  We consider continuum random Schr\"odinger operators of the type 
$H_{\omega} = -\Delta + V_0 + V_{\omega}$ with a deterministic 
background potential $V_0$. We establish criteria for the absence 
of continuous and absolutely continuous spectrum, respectively, 
outside the spectrum of $-\Delta +V_0$. The models we treat 
include random surface potentials as well as sparse or slowly 
decaying random potentials. In particular, we establish absence of 
absolutely continuous surface spectrum for random potentials 
supported near a one-dimensional surface (``random tube'') in 
arbitrary dimension.