Scale-free uncertainty principles and Wegner estimates for random breather potentials
Analysis of PDEs
2016-01-07 v4
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, and Klein. 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.
Cite
@article{arxiv.1410.5273,
title = {Scale-free uncertainty principles and Wegner estimates for random breather potentials},
author = {Ivica Nakić and Matthias Täufer and Martin Tautenhahn and Ivan Veselić},
journal= {arXiv preprint arXiv:1410.5273},
year = {2016}
}