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On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials

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Abstract

We consider discrete one-dimensional random Schrödinger operators with decaying matrix-valued, independent potentials. We show that if the ℓ2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schrödinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schrödinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon et al. (Ann. Inst. H. Poincaré Phys. Théor. 42(3):283–309, 1985).

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Richard Froese

  2. Department of Mathematics, College of William & Mary, Williamsburg, Virginia, USA

    David Hasler

  3. Fakultät für Mathematik und Informatik, FernUniversität Hagen, Hagen, Germany

    Wolfgang Spitzer

Authors
  1. Richard Froese
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  2. David Hasler
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  3. Wolfgang Spitzer
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Correspondence to David Hasler.

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Froese, R., Hasler, D. & Spitzer, W. On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials. Math Phys Anal Geom 13, 219–233 (2010). https://doi.org/10.1007/s11040-010-9076-9

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  • DOI: https://doi.org/10.1007/s11040-010-9076-9

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