Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian

DOI10.1007/s00220-011-1220-2zbMath1232.81016arXiv1001.2552OpenAlexW3103452856MaRDI QIDQ634625

David Damanik, A. S. Gorodetskii

Publication date: 16 August 2011

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

Full work available at URL: https://arxiv.org/abs/1001.2552

Mathematics Subject Classification ID

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)

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Cites Work

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• Hölder foliations
• Power-law bounds on transfer matrices and quantum dynamics in one dimension. II
• Combinatorial rigidity for unicritical polynomials
• Bers and Hénon, Painlevé and Schrödinger
• Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
• Almost periodic Schrödinger operators. II: The integrated density of states
• Spectral properties of a tight binding Hamiltonian with period doubling potential
• The fractal dimension of the spectrum of the Fibonacci Hamiltonian
• Quantum dynamics via complex analysis methods: general upper bounds without time-averaging and tight lower bounds for the strongly coupled Fibonacci Hamiltonian
• Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
• The spectrum of a quasiperiodic Schrödinger operator
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Structural stability of diffeomorphisms on two-manifolds
• Power law growth for the resistance in the Fibonacci model
• Power-law bounds on transfer matrices and quantum dynamics in one dimension
• Hausdorff dimension of spectrum of one-dimensional Schrödinger operator with Sturmian potentials
• Subdiffusive quantum transport for 3D Hamiltonians with absolutely continuous spectra
• Uniform spectral properties of one-dimensional quasicrystals. III: \(\alpha\)-continuity.
• Uniform spectral properties of one-dimensional quasicrystals. II: The Lyapunov exponent.
• Uniform spectral properties of one-dimensional quasicrystals. I: Absence of eigenvalues
• Operators with singular continuous spectrum. VII: Examples with borderline time decay
• The spectrum of the weakly coupled Fibonacci Hamiltonian
• The absolutely continuous spectrum of one-dimensional Schrödinger operators
• Some remarks on discrete aperiodic Schrödinger operators
• Quantum dynamics and decompositions of singular continuous spectra
• On the sum and product of continued fractions
• Sums of numbers with small partial quotients
• JACOBI MATRICES WITH RANDOM POTENTIALS TAKING FINITELY MANY VALUES
• The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces
• Hausdorff dimension for horseshoes
• Upper bounds in quantum dynamics
• Curves of fixed points of trace maps
• GAP LABELLING THEOREMS FOR ONE DIMENSIONAL DISCRETE SCHRÖDINGER OPERATORS
• Results on Sums of Continued Fractions
• TRACE MAPS, INVARIANTS, AND SOME OF THEIR APPLICATIONS
• Renormalization of Quasiperiodic Mappings
• Cantor sets and numbers with restricted partial quotients
• Remarks on the spectral properties of tight-binding and Kronig-Penney models with substitution sequences
• Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior
• Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian
• On M. Hall's Continued Fraction Theorem
• Invariant manifolds
• Sums of numbers with small partial quotients. II