Gibbs-like measure for spectrum of a class of quasi-crystals
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Publication:2884093
DOI10.1017/S0143385710000635zbMath1242.81067MaRDI QIDQ2884093
Qing-Hui Liu, Zhi-Ying Wen, Shen Fan
Publication date: 24 May 2012
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Difference operators (39A70) Continued fractions (11A55) Linear difference operators (47B39)
Related Items (7)
The spectral properties of the strongly coupled Sturm Hamiltonian of eventually constant type ⋮ Schrödinger operators with dynamically defined potentials ⋮ The fractal dimensions of the spectrum of Sturm Hamiltonian ⋮ Cookie-Cutter-Like Dynamic System of Unbounded Expansion ⋮ Almost sure frequency independence of the dimension of the spectrum of Sturmian Hamiltonians ⋮ Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian ⋮ Transport exponents of Sturmian Hamiltonians
Cites Work
- The fractal dimension of the spectrum of the Fibonacci Hamiltonian
- Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
- Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions
- Some dimensional results for homogeneous Moran sets
- Hausdorff dimension of spectrum of one-dimensional Schrödinger operator with Sturmian potentials
- Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity.
- On the structures and dimensions of Moran sets
- Measure zero spectrum of a class of Schrödinger operators
- Dimensions of cookie-cutter-like sets
- Spectral properties of one dimensional quasi-crystals
- Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
- Dimension of the spectrum of one-dimensional discrete Schrödinger operators with Sturmian potentials
- On dimensions of multitype Moran sets
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