Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators

摘要: We prove exponential localization at all energies for two types of one-dimensional random Schr6dinger operators: the Poisson model and displacement model. As opposed to Anderson-type models, these operators are not monotonic in parameters. Therefore classical one-parameter version spectral averaging, as used proofs Anderson breaks down. use new method two-parameter averaging apply it well case. In addition, we results from inverse theory, which show that works sufficiently many (all but a discrete set) conclude energies.