Abstract
The paper considers the class of Schrödinger multidimensional discrete operators with quasi-periodic unbounded potential for which essentially complete spectral analysis may be carried out. In the case of sufficiently high incommensurability of almost-periods, the spectrum of such operators is found to be pure point and simple, the eigenfunctions exponentially localized and the low frequency conductivity exponentially small. In the one-dimensional case, for any incommensurability, the spectrum does not contain the absolutely continuous component, while for small incommensurability the spectrum is singular continuous.
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Communicated by Ya. G. Sinai
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Figotin, A.L., Pastur, L.A. An exactly solvable model of a multidimensional incommensurate structure. Commun.Math. Phys. 95, 401–425 (1984). https://doi.org/10.1007/BF01210831
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DOI: https://doi.org/10.1007/BF01210831