Spectral transitions for the square Fibonacci Hamiltonian
type: Item
instance of: scholarly article
title: Spectral transitions for the square Fibonacci Hamiltonian
zbMATH Open document ID: 1503.47059
DOI: 10.4171/JST/232
author: David Damanik
author: Anton Gorodetski
published in: Journal of Spectral Theory
publication date: 2018-11-15T00:00:00Z
review text: Summary: 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 states measure coexist. This provides the first physically relevant example exhibiting this phenomenon.
Mathematics Subject Classification ID: 47B93
Mathematics Subject Classification ID: 47B36
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 6979900
zbMATH Keywords: square Fibonacci Hamiltonian
zbMATH Keywords: spectral transitions
zbMATH Keywords: quasicrystals
MaRDI profile type: Publication
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Wikidata QID: Q129060247
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description: scientific article; zbMATH DE number 6979900