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

We prove a localization theorem for continuous ergodic Schrödinger operators $H_ω:= H_0 + V_ω$, where the random potential $V_ω$ is a nonnegative Anderson-type perturbation of the periodic operator $H_0$. We consider a lower spectral band edge of $σ(H_0)$, say $E= 0$, at a gap which is preserved by the perturbation $V_ω$. 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 $H_ω$ has only pure point spectrum in $I$ for almost all $ω$.

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