Localization for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues
نویسنده
چکیده
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.
منابع مشابه
Localisation for random perturbations of periodic Schrödinger operators with regular Floquet eigenvalues∗
We prove a localisation theorem for continuous ergodic Schrödinger operators Hω := H0 + Vω, where the random potential Vω is a nonnegative Anderson-type random 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 m...
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