Abstract
In this paper we prove that the one dimensional Schrödinger operator onl 2(ℤ) with potential given by:
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 allEquationSource % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadIhaiiaacq% WFiiIZtuuDJXwAK1uy0HMmaeHbfv3ySLgzG0uy0HgiuD3BaGqbbiab% +nj8ubaa!4628!\[x \in \mathbb{T}$$ .
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Bellissard, J., Iochum, B., Scoppola, E. et al. Spectral properties of one dimensional quasi-crystals. Commun. Math. Phys. 125, 527–543 (1989). https://doi.org/10.1007/BF01218415
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DOI: https://doi.org/10.1007/BF01218415