Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian

Abstract

We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

28 pages, to appear in Duke Math. J

References in corpus (7)

• The Fibonacci Hamiltonian
• Electronic Energy Spectra of Square and Cubic Fibonacci Quasicrystals
• Electronic energy spectra and wave functions on the square Fibonacci tiling
• Spectra of Discrete Schrödinger Operators with Primitive Invertible Substitution Potentials
• Wave Functions, Quantum Diffusion, and Scaling Exponents in Golden-Mean Quasiperiodic Tilings
• Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators
• Bloch-like Electronic Wave Functions in Two-Dimensional Quasicrystals

Cited by in corpus (16)

• The Fibonacci Hamiltonian
• Spectral Continuity for Aperiodic Quantum Systems I. General Theory
• Products of two Cantor sets
• What is Aperiodic Order?
• Quantum and Spectral Properties of the Labyrinth Model
• Singularly continuous spectrum of a self-similar Laplacian on the half-line
• Conditions for the difference set of a central Cantor set to be a Cantorval
• When the algebraic difference of two central Cantor sets is an interval?
• On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics
• Hausdorff dimension of the spectrum of the square Fibonacci Hamiltonian
• On the spectra of separable 2D almost Mathieu operators
• Sums of two homogeneous Cantor sets
• A model for reducing the angulon operator
• Sums of two self-similar Cantor sets
• Diffusion on Delone sets
• Newhouse phenomena in the Fibonacci trace map