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

Abstract

We prove a localization theorem for continuous ergodic Schrödinger operators $H_{\omega }:=H_0+V_{\omega }$, where the random potential $V_{\omega }$ is a nonnegative Anderson-type perturbation of the periodic operator $H_0$. We consider a lower spectral band edge of $\sigma (H_0)$, say $E=0$, at a gap which is preserved by the perturbation $V_{\omega }$. Assuming that all Floquet eigenvalues of $H_0$, 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 $H_{\omega }$ has only pure point spectrum in $I$ for almost all $\omega$.

21 pages

References in corpus (1)

• Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space

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