Matthias Täufer

Wegner estimate for the random breather model

We prove a Wegner estimate for the random breather model: a class of random Schrödinger operators −∆+V_ω where the potential V_ω(x) =∑_{j \in Z^d} u((x−j)/ω_j) consists of a sum of random dilations of a single-site potential u at each lattice site j \in Z^d.
The random breather model is an example of a random Schrödinger operator where the random potential depends in a non-linear manner on elementary random variables.
One main ingredient in the proof are lower estimates on the sensitivity of eigenvalues with respect to certain perturbations which themselves follow from recent quantitative unique continuation principles for spectral projectors of Schrödinger operators.
Together with initial scale estimates, recently proved by C. Schumacher and
I. Veselić (both Dortmund), we conclude Anderson localization for this model at the bottom of the spectrum.
Based on joint work with I. Nakic (Zagreb), M. Tautenhahn (Chemnitz), and I. Veselić (Dortmund).