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Journal of Spectral Theory

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Volume 8, Issue 4, 2018, pp. 1487–1507
DOI: 10.4171/JST/232

Published online: 2018-10-22

Spectral transitions for the square Fibonacci Hamiltonian

David Damanik[1] and Anton Gorodetski[2]

(1) Rice University, Houston, USA
(2) University of California, Irvine, USA

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.

Keywords: Square Fibonacci Hamiltonian, spectral transitions, quasicrystals

Damanik David, Gorodetski Anton: Spectral transitions for the square Fibonacci Hamiltonian. J. Spectr. Theory 8 (2018), 1487-1507. doi: 10.4171/JST/232