Localisation for Random Perturbations of Periodic Schrödinger Operators with Regular Floquet Eigenvalues (2000)
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BibTeX
@MISC{Veselic00localisationfor,
author = {Ivan Veselic},
title = {Localisation for Random Perturbations of Periodic Schrödinger Operators with Regular Floquet Eigenvalues},
year = {2000}
}
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Abstract
We prove a localisation theorem for continuous ergodic Schrödinger operators H! := H0 + V! , where the random potential V! is a nonnegative Anderson-type random perturbation of the periodic operator H0 . We consider a lower spectral band edge of (H0 ), say E = 0, at a gap which is preserved by the perturbation V! . 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 H! has only pure point spectrum in I for almost all !.
