JournalsjstVol. 1, No. 4pp. 409–442

Ballistic behavior for random Schrödinger operators on the Bethe strip

  • Abel Klein

    University of California, Irvine, United States
  • Christian Sadel

    Pontificia Universidad Católica de Chile, Santiago De Chile, Chile
Ballistic behavior for random Schrödinger operators on the Bethe strip cover
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Abstract

The Bethe strip of width mm is the Cartesian product B×{1,,m}\mathbb B\times\{1,\ldots,m\}, where B\mathbb B is the Bethe lattice (Cayley tree). We consider Anderson-like Hamiltonians   Hλ=12Δ1+1A+λV\;H_\lambda=\frac12 \Delta \otimes 1 + {1 \otimes A}+\lambda \mathcal{V} on a Bethe strip with connectivity K2K \ge 2, where AA is an m×mm\times m symmetric matrix, V\mathcal{V} is a random matrix potential, and λ\lambda is the disorder parameter. Under certain conditions on AA and KK, for which we previously proved the existence of absolutely continuous spectrum for small λ\lambda, we now obtain ballistic behavior for the spreading of wave packets evolving under HλH_\lambda for small λ\lambda.

Cite this article

Abel Klein, Christian Sadel, Ballistic behavior for random Schrödinger operators on the Bethe strip. J. Spectr. Theory 1 (2011), no. 4, pp. 409–442

DOI 10.4171/JST/18