Continuity properties of the electronic spectrum of 1D quasicrystals

DOI10.1007/BF02101510zbMath0754.46049MaRDI QIDQ1181849

Daniel Testard, Jean Bellissard, Bruno Iochum

Publication date: 27 June 1992

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

zbMATH Keywords

\(C^*\)-algebraquasiperiodic potentialelectronic spectrumOstlund- Kim spectrum

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of selfadjoint operator algebras to physics (46L60) Renormalization group methods applied to problems in quantum field theory (81T17) Applications of functional analysis in quantum physics (46N50) Applications of statistical mechanics to specific types of physical systems (82D99)

Related Items (15)

Bulk-boundary correspondence for Sturmian Kohmoto-like models ⋮ Non-commutative methods for the K-theory of \(C^*\)-algebras of aperiodic patterns from cut-and-project systems ⋮ Delone dynamical systems and spectral convergence ⋮ Electronic transport properties of quasicrystals ⋮ Some remarks on discrete aperiodic Schrödinger operators ⋮ Spectral continuity for aperiodic quantum systems I. General theory ⋮ Continuity of the spectrum of a field of self-adjoint operators ⋮ Spectral continuity for aperiodic quantum systems: Applications of a folklore theorem ⋮ Power law growth for the resistance in the Fibonacci model ⋮ Continuity of Spectra in Rieffel’s Pseudodifferential Calculus ⋮ Hölder continuity of the spectra for aperiodic Hamiltonians ⋮ On the continuity of spectra for families of magnetic pseudodifferential operators ⋮ Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians ⋮ Lipschitz continuity of gap boundaries for Hofstadter-like spectra ⋮ Transport exponents of Sturmian Hamiltonians

Cites Work

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• Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
• Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
• Spectral properties of one dimensional quasi-crystals
• Topological representation of \(C^ *\)-algebras
• Renormalization of Quasiperiodic Mappings

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