JournalsprimsVol. 40, No. 1pp. 29–90

Wegner Estimates and Localization for Gaussian Random Potentials

  • Naomasa Ueki

    Kyoto University, Japan
Wegner Estimates and Localization for Gaussian Random Potentials cover
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Abstract

A Wegner estimate is proven for a Schr¨dinger operator with a bounded random o vector potential and a Gaussian random scalar potential. The estimate is used to prove the strong dynamical localization and the exponential decay of the eigenfunctions. For the proof, Klopp’s method using a vector field on a probability space and Germinet and Klein’s bootstrap multiscale analysis are applied. Moreover Germinet and Klein’s characterization of the Anderson metal-insulator transport transition is extended to the above operator.

Cite this article

Naomasa Ueki, Wegner Estimates and Localization for Gaussian Random Potentials. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 29–90

DOI 10.2977/PRIMS/1145475966