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Article
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as
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Article
Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign
Let H be a one-dimensional discrete Schrödinger operator. We prove that if Σ ess (H)⊂[−2,2], then H−H 0 is compact and Σ ess
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Article
Linearly Recurrent Circle Map Subshifts and an Application to Schrödinger Operators
We discuss circle map sequences and subshifts generated by them. We give a characterization of those sequences among them which are linearly recurrent. As an application we deduce zero-measure spectrum for a ...
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Article
A Palindromic Half-Line Criterion for Absence of Eigenvalues and Applications to Substitution Hamiltonians
We prove a criterion for absence of decaying solutions on the half-line for one-dimensional discrete Schrödinger operators. As necessary inputs, we require infinitely many palindromic prefixes and upper and l...
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Article
Multi-scale analysis implies strong dynamical localization
We prove that a strong form of dynamical localization follows from a variable energy multi-scale analysis. This abstract result is applied to a number of models for wave propagation in disordered media.
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Article
Linear Repetitivity, I. Uniform Subadditive Ergodic Theorems and Applications
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extend...
