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Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

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Abstract:

 We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrödinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamiltonian.

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Authors and Affiliations

  1. Department of Mathematics 253–37, California Institute of Technology, Pasadena, CA 91125, USA. E-mail: damanik@its.caltech.edu, , , , , , US

    David Damanik

  2. UMR 6628 – MAPMO, Université d'Orleans, B.P. 6759, 45067 Orleans Cédex, France. E-mail: serguei.tcherem@labomath.univ-orleans.fr, , , , , , FR

    Serguei Tcheremchantsev

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  1. David Damanik
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  2. Serguei Tcheremchantsev
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Received: 5 June 2002 / Accepted: 20 January 2003 Published online: 28 March 2003

RID="⋆"

ID="⋆" D.D. was supported in part by NSF Grant No. DMS–0227289

Communicated by M. Aizenman

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Damanik, D., Tcheremchantsev, S. Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension. Commun. Math. Phys. 236, 513–534 (2003). https://doi.org/10.1007/s00220-003-0824-6

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  • DOI: https://doi.org/10.1007/s00220-003-0824-6

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