Matthias Täufer, Ivan Veselić: Conditional Wegner estimate for the standard random breather potential

Author(s):

Matthias Täufer
Ivan Veselić

Title:

Matthias Täufer, Ivan Veselić: Conditional Wegner estimate for the standard random breather potential

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 07, 2014

Mathematics Subject Classification:

    60H25 []
    35J10 []

Abstract:

We prove a conditional Wegner estimate for Schr\"odinger operators with random potentials of breather type. More precisely, we reduce the proof of the Wegner estimate to a scale free unique continuation principle. The relevance of such unique continuation principles has been emphasized in previous papers, in particular in recent years. We consider the \emph{standard} breather model, meaning that the single site potential is the characteristic function of a ball or a cube. While our methods work for a substantially larger class of random breather potentials, we discuss in this particular paper only the standard model in order to make the arguments and ideas easily accessible.

Keywords:

Language:

English

Publication time:

06/2014