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Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schrödinger Equation

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Abstract

Starting from results already obtained for quasi-periodic co-cycles in \(SL(2, \mathbb R),\) we show that the rotation number of the one-dimensional time-continuous Schrödinger equation with Diophantine frequencies and a small analytic potential has the behavior of a \(\frac{1}{2}-\)Hölder function. We give also a sub-exponential estimate of the length of the gaps which depends on its label given by the gap-labeling theorem.

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  1. Ecole Nationale d’Ingénieurs de Monastir, Avenue Ibn Eljazzar, 5019, Monastir, Tunisia

    Sana Hadj Amor

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  1. Sana Hadj Amor
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Correspondence to Sana Hadj Amor.

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Amor, S.H. Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schrödinger Equation. Math Phys Anal Geom 15, 331–342 (2012). https://doi.org/10.1007/s11040-012-9113-y

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  • DOI: https://doi.org/10.1007/s11040-012-9113-y

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