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Limit-periodic Schrödinger operators with uniformly localized eigenfunctions

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Abstract

We exhibit limit-periodic Schrödinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of eigenvectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization.

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Authors and Affiliations

  1. Department of Mathematics, Rice University, Houston, TX, 77005, USA

    David Damanik & Zheng Gan

Authors
  1. David Damanik
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  2. Zheng Gan
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Correspondence to David Damanik.

Additional information

D. D. and Z. G. were supported in part by NSF grant DMS-0800100.

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Damanik, D., Gan, Z. Limit-periodic Schrödinger operators with uniformly localized eigenfunctions. JAMA 115, 33–49 (2011). https://doi.org/10.1007/s11854-011-0022-y

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  • DOI: https://doi.org/10.1007/s11854-011-0022-y

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