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Phase Transition and Semi-Global Reducibility

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Abstract

For 1D continuous Schödinger operators with large analytic quasi-periodic potentials of two frequencies, one knows that the spectral measure is singular at the bottom of the spectrum and purely absolutely continuous in the upper part of the spectrum, so there is a phase transition when energy increases. In this paper, we obtain the exact power-law for the phase transition in energy by the semi-global reducibility theory of analytic quasi-periodic linear systems.

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Author notes

  1. Qi Zhou

    Present address: Laboratoire de Probabilités et Modèles aléatoires, Université Pierre et Marie Curie, Boite courrier 188, 75252, Paris Cedex 05, France

Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Jiangong You & Qi Zhou

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  1. Jiangong You
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  2. Qi Zhou
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Correspondence to Qi Zhou.

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Communicated by B. Simon

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You, J., Zhou, Q. Phase Transition and Semi-Global Reducibility. Commun. Math. Phys. 330, 1095–1113 (2014). https://doi.org/10.1007/s00220-014-2012-2

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