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The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

Damanik, David and Embree, Mark and Gorodetski, Anton and Tcheremchantsev, Serguei (2008) The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian. Communications in Mathematical Physics, 280 (2). pp. 499-516. ISSN 0010-3616. doi:10.1007/s00220-008-0451-3.

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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 λ→∞,dim(σ(Hλ))⋅logλ converges to an explicit constant, log(1+2–√)≈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.

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Damanik, David0000-0001-5924-3849
Additional Information:© 2008 Springer-Verlag. Received: 2 May 2007; Accepted: 20 August 2007; First Online: 04 March 2008. D. D. was supported in part by NSF grant DMS-0653720. M. E. was supported by NSF grant DMS-CAREER-0449973 We are grateful for the On-Line Encylopedia of Integer Sequences and the Inverse Symbolic Calculator, both of which assisted our hunt for f∗.
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Subject Keywords:Fractal Dimension; Hausdorff Dimension; Transfer Matrice; Singular Continuous Spectrum; Periodic Spectrum
Issue or Number:2
Record Number:CaltechAUTHORS:20191107-141242740
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Official Citation:Damanik, D., Embree, M., Gorodetski, A. et al. Commun. Math. Phys. (2008) 280: 499.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99743
Deposited By: Tony Diaz
Deposited On:08 Nov 2019 12:53
Last Modified:16 Nov 2021 17:48

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