Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian

DOI10.1215/00127094-3119739zbMath1358.37117arXiv1306.4284OpenAlexW1560763334MaRDI QIDQ2354142

David Damanik, A. S. Gorodetskii, B. M. Solomyak

Publication date: 10 July 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.4284

zbMATH Keywords

Lyapunov exponentsquasicrystalshyperbolic measuresFibonacci Hamiltoniandensity of states measureconvolutions of singular measures

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Dimension theory of smooth dynamical systems (37C45) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (18)

When the algebraic difference of two central Cantor sets is an interval? ⋮ Spectral transitions for the square Fibonacci Hamiltonian ⋮ Quantum and spectral properties of the Labyrinth model ⋮ Diffusion on Delone sets ⋮ On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics ⋮ Conditions for the difference set of a central Cantor set to be a Cantorval ⋮ Delone dynamical systems and spectral convergence ⋮ Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set ⋮ Spectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017 ⋮ Spectral continuity for aperiodic quantum systems I. General theory ⋮ The Fibonacci Hamiltonian ⋮ Sums of two homogeneous Cantor sets ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ On the spectra of separable 2D almost Mathieu operators ⋮ Spectral continuity for aperiodic quantum systems: Applications of a folklore theorem ⋮ Sums of two self-similar Cantor sets ⋮ Spectra of discrete two-dimensional periodic Schrödinger operators with small potentials ⋮ Stable intersection of Cantor sets in higher dimension and robust homoclinic tangency of the largest codimension

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