Localization for random perturbations of periodic Schroedinger operators with regular Floquet eigenvalues

Original · EN

We prove a localization theorem for continuous ergodic Schrödinger operators Hω:= H₀ + Vω, where the random potential Vω is a nonnegative Anderson-type perturbation of the periodic operator H₀. We consider a lower spectral band edge of σ(H₀), say E= 0, at a gap which is preserved by the perturbation Vω. Assuming that all Floquet eigenvalues of H₀, which reach the spectral edge 0 as a minimum, have there a positive definite Hessian, we conclude that there exists an interval I containing 0 such that Hω has only pure point spectrum in I for almost all ω.