Spectral transitions for the square Fibonacci Hamiltonian

  • David Damanik

    Rice University, Houston, USA
  • Anton Gorodetski

    University of California, Irvine, USA
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Abstract

We study the spectrum and the density of states measure of the square Fibonacci Hamiltonian. We describe where the transitions from positive-measure to zero-measure spectrum and from absolutely continuous to singular density of states measure occur. This shows in particular that for almost every parameter from some open set, a positive-measure spectrum and a singular density of statesmeasure coexist. This provides the first physically relevant example exhibiting this phenomenon.

Cite this article

David Damanik, Anton Gorodetski, Spectral transitions for the square Fibonacci Hamiltonian. J. Spectr. Theory 8 (2018), no. 4, pp. 1487–1507

DOI 10.4171/JST/232