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Lower Transport Bounds for One-dimensional Continuum Schrödinger Operators

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Abstract

We prove quantum dynamical lower bounds for one-dimensional continuum Schrödinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states. This general result is applied to a number of models, including the Bernoulli–Anderson model with a constant single-site potential.

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Authors and Affiliations

  1. Mathematics 253–37, California Institute of Technology, Pasadena, CA, 91125, USA

    David Damanik

  2. Fakultät für Mathematik, TU Chemnitz, Chemnitz, 09107, Germany

    Daniel Lenz

  3. Department of Mathematics, University of Alabama, Birmingham, AL, 35294, USA

    Günter Stolz

Authors
  1. David Damanik
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  2. Daniel Lenz
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  3. Günter Stolz
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Correspondence to David Damanik.

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Dedicated to Joachim Weidmann on the occasion of his 65th birthday

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Damanik, D., Lenz, D. & Stolz, G. Lower Transport Bounds for One-dimensional Continuum Schrödinger Operators. Math. Ann. 336, 361–389 (2006). https://doi.org/10.1007/s00208-006-0006-x

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