JournalsjstVol. 6, No. 3pp. 557–600

Localization for transversally periodic random potentials on binary trees

  • Richard Froese

    The University of British Columbia, Vancouver, Canada
  • Darrick Lee

    The University of British Columbia, Vancouver, Canada
  • Christian Sadel

    Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
  • Wolfgang Spitzer

    FernUniversität Hagen, Germany
  • Günter Stolz

    University of Alabama at Birmingham, USA
Localization for transversally periodic random potentials on binary trees cover

A subscription is required to access this article.

Abstract

We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, QrQ_r, and a random transversally periodic potential, κQt\kappa Q_t, with coupling constant κ\kappa. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ\kappa. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ\kappa. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder.

Cite this article

Richard Froese, Darrick Lee, Christian Sadel, Wolfgang Spitzer, Günter Stolz, Localization for transversally periodic random potentials on binary trees. J. Spectr. Theory 6 (2016), no. 3, pp. 557–600

DOI 10.4171/JST/132