Absolutely continuous spectrum and spectral transition for some continuous random operators

Details Absolutely continuous spectrum and spectral transition for some continuous random operators Absolutely continuous spectrum and spectral transition for some continuous random operators

2011-02-21

arxiv.org/abs/1102.4130v1

Physics

Mathematical Physics

Scientific paper

In this paper we consider two classes of random Hamiltonians on $L^2(\RR^d)$ one that imitates the lattice case and the other a Schr\"odinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for the Anderson model in higher dimension.

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