 98569 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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