Abstract.
We consider continuum random Schrödinger operators of the type Hω = −Δ + V0 + Vω with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of −Δ + V0. 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Jens Marklof
submitted 07/04/04, accepted 19/08/04
Rights and permissions
About this article
Cite this article
Boutet de Monvel, A., Stollmann, P. & Stolz, G. Absence of Continuous Spectral Types for Certain Non-Stationary Random Schrödinger Operators. Ann. Henri Poincaré 6, 309–326 (2005). https://doi.org/10.1007/s00023-005-0208-x
Issue Date:
DOI: https://doi.org/10.1007/s00023-005-0208-x