Singular continuous spectrum for a class of substitution Hamiltonians

DOI10.1023/A:1007510721504zbMath0930.11007OpenAlexW4231749704MaRDI QIDQ1281576

David Damanik

Publication date: 14 February 2000

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1007510721504

zbMATH Keywords

quasicrystalsone-dimensional Schrödinger operatorsingular continuous spectrumprimitive substitutive sequencesubstitution Hamiltonians

Mathematics Subject Classification ID

Combinatorics on words (68R15) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Automata sequences (11B85) Linear difference operators (47B39)

Related Items (14)

On the spectra of Pisot-cyclotomic numbers ⋮ Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals ⋮ Delone dynamical systems and spectral convergence ⋮ Schrödinger operators with dynamically defined potentials ⋮ Local symmetries in the period-doubling sequence ⋮ Singular continuous spectrum for a class of nonprimitive substitution Schrödinger operators ⋮ Invariants of the trace map and uniform spectral properties for discrete Sturmian Dirac operators ⋮ Substitution dynamical systems: characterization of linear repetitivity and applications ⋮ A version of Gordon’s theorem for multi-dimensional Schrödinger operators ⋮ Uniform spectral properties of one-dimensional quasicrystals. IV. Quasi-Sturmian potentials ⋮ A nonprimitive substitution Schrödinger operator with generic singular continuous spectrum ⋮ Substitution Hamiltonians with bounded trace map orbits ⋮ Computing Spectral Measures of Self-Adjoint Operators ⋮ On a question of Hof, Knill and Simon on palindromic substitutive systems

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