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The rotation number for finite difference operators and its properties

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Abstract

We discuss a rotation number α(λ) for second order finite difference operators. Ifk(λ) denotes the integrated density of states, thenk(λ)=2α(λ). For almost periodic operators,k(λ) is proved to lie in the frequency-module whenever λ is outside the spectrum; this yields a labelling of the gaps of the spectrum.

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  1. Centre de Physique Théorique de l'Ecole Polytechnique, Plateau de Palaiseau, F-91128, Palaiseau, Cedex, France

    F. Delyon & B. Souillard

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  1. F. Delyon
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  2. B. Souillard
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Communicated by B. Simon

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Delyon, F., Souillard, B. The rotation number for finite difference operators and its properties. Commun.Math. Phys. 89, 415–426 (1983). https://doi.org/10.1007/BF01214663

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  • DOI: https://doi.org/10.1007/BF01214663

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