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Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

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Abstract

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden

    L. H. Eliasson

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  1. L. H. Eliasson
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Communicated by Ya. G. Sinai

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Eliasson, L.H. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Commun.Math. Phys. 146, 447–482 (1992). https://doi.org/10.1007/BF02097013

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  • DOI: https://doi.org/10.1007/BF02097013

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