I. Nakić, M. Täufer, M. Tautenhahn, Ivan Veselić: Scale-free uncertainty principles and Wegner estimates for random breather potentials

Author(s):

I. Nakić
M. Täufer
M. Tautenhahn
Ivan Veselić

Title:

I. Nakić, M. Täufer, M. Tautenhahn, Ivan Veselić: Scale-free uncertainty principles and Wegner estimates for random breather potentials

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2014

Mathematics Subject Classification:

    35J10 []
    35R60 []
    35A23 []

Abstract:

We present new scale-free quantitative unique continuation principles for Schr\"odinger operators. They apply to linear combinations of eigenfunctions corresponding to eigenvalues below a prescribed energy, and can be formulated as an uncertainty principle for spectral projectors. This extends recent results of Rojas-Molina \& Veseli'c \cite{RojasMolinaV-13}, and Klein \cite{Klein-13}. We apply the scale-free unique continuation principle to obtain a Wegner estimate for a random Schr\"odinger operator of breather type. It holds for arbitrarily high energies. Schr\"odinger operators with random breather potentials have a non-linear dependence on random variables. We explain the challenges arising from this non-linear dependence.

Keywords:

Language:

English

Publication time:

10/2014