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Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading

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Abstract

We establish quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds following a scaling law. As a consequence, we obtain improved dynamical results for the Fibonacci Hamiltonian and related models.

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Authors and Affiliations

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

    David Damanik

  2. UMR 6628-MAPMO, Université d'Orléans, B.P. 6759, F-45067, Orléans Cedex, France

    Serguei Tcheremchantsev

Authors
  1. David Damanik
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  2. Serguei Tcheremchantsev
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Corresponding author

Correspondence to David Damanik.

Additional information

D. D. was supported in part by NSF grant DMS-0227289.

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Damanik, D., Tcheremchantsev, S. Scaling estimates for solutions and dynamical lower bounds on wavepacket spreading. J. Anal. Math. 97, 103–131 (2005). https://doi.org/10.1007/BF02807404

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  • DOI: https://doi.org/10.1007/BF02807404

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