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On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials

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Abstract

We prove that a linear d-dimensional Schrödinger equation with an x-periodic and t-quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of x-periodic functions. This transformation is a quasiperiodic function of t.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris 7, Case 7052, 2 place Jussieu, Paris, France

    Håkan L. Eliasson

  2. École polytechnique, Palaiseau, France

    Sergei B. Kuksin

  3. Department of Mathematics, Heriot-Watt University, Edinburgh, UK

    Sergei B. Kuksin

Authors
  1. Håkan L. Eliasson
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  2. Sergei B. Kuksin
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Correspondence to Sergei B. Kuksin.

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Communicated by A. Kupiainen

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Eliasson, H.L., Kuksin, S.B. On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials. Commun. Math. Phys. 286, 125–135 (2009). https://doi.org/10.1007/s00220-008-0683-2

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  • DOI: https://doi.org/10.1007/s00220-008-0683-2

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