Communications in Mathematical Physics

, Volume 280, Issue 2, pp 499–516 | Cite as

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

  • D. Damanik
  • M. Embree
  • A. Gorodetski
  • S. Tcheremchantsev


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 \(\lambda \to \infty, {\rm dim} (\sigma(H_\lambda)) \cdot {\rm log} \lambda\)converges to an explicit constant, \({\rm log}(1+\sqrt{2})\approx 0.88137\) . We also discuss consequences of these results for the rate of propagation of a wavepacket that evolves according to Schrödinger dynamics generated by the Fibonacci Hamiltonian.


Fractal Dimension Hausdorff Dimension Transfer Matrice Singular Continuous Spectrum Periodic Spectrum 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • D. Damanik
    • 1
  • M. Embree
    • 2
  • A. Gorodetski
    • 3
  • S. Tcheremchantsev
    • 4
  1. 1.Department of MathematicsRice UniversityHoustonUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA
  3. 3.Mathematics 253-37California Institute of TechnologyPasadenaUSA
  4. 4.Université d’Orléans, Laboratoire MAPMO, CNRS-UMR 6628Orléans CedexFrance

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