Localization for random Schrödinger operators on \(L^ 2 (\mathbb{R}^ d)\): a semiclassical model
In \(L^ 2 ({\mathbb{R}}^ d)\), we prove exponential localization for a semi- classical periodic Schrödinger operator perturbated by small independent identically distributed random perturbations put in each well of the periodic potential. To do this, we first show that our operator, restricted to some suitably chosen energy interval, is unitarily equivalent to an infinite random matrix with coefficients we can control. Then, for this type of random matrices, we prove an Anderson localization theorem. We also apply this result to prove localization at large energy or large disorder, for long range discrete Anderson models.
scientific article; zbMATH DE number 745228
scientific article