98-569 Veseli\'c, Ivan
Localisation for random perturbations of periodic Schr\"odinger operators with regular Floquet eigenvalues (314K, ps) Aug 21, 98
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Abstract. We prove a localisation theorem for the ergodic Schr\"odinger operator $H_\omega := H_0 + V_\omega$ on $L^2 (\RR^d)$. Here $V_\omega := \sum_{k \in \ZZ^d} \omega_k \, u( \cdot - k)$ is a nonnegative Anderson type random 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 perserved 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 $I \ni 0$ such that $H_\omega$ has only pure point spectrum in $I$ for almost all $\omega$.

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