Spectral properties of one dimensional quasi-crystals |
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Authors: | J Bellissard B Iochum E Scoppola D Testard |
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Institution: | 1. Université de Provence, Marseille 2. Centre de Physique Theorique, CNRS, Luminy Case 907, F-13288, Marseille Cedex 9, France 3. Dip. Fisica, Università di Roma “La Sapienza”, Ple A. Moro 2, I-00185, Roma, Italy 4. Université d'Aix, Marseille 2, Luminy
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Abstract: | In this paper we prove that the one dimensional Schrödinger operator onl 2(?) with potential given by: $$\upsilon (n) = \lambda \chi _{1 - \alpha , 1} (x + n\alpha )\alpha \notin \mathbb{Q}$$ has a Cantor spectrum of zero Lebesgue measure for any irrationalα and any λ>0. We can thus extend the Kotani result on the absence of absolutely continuous spectrum for this model, to all . |
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