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. https://resolver.caltech.edu/CaltechAUTHORS:20191107-141242740
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Abstract
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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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 | ||||||||||||
DOI: | 10.1007/s00220-008-0451-3 | ||||||||||||
Record Number: | CaltechAUTHORS:20191107-141242740 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20191107-141242740 | ||||||||||||
Official Citation: | Damanik, D., Embree, M., Gorodetski, A. et al. Commun. Math. Phys. (2008) 280: 499. https://doi.org/10.1007/s00220-008-0451-3 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 99743 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 08 Nov 2019 12:53 | ||||||||||||
Last Modified: | 16 Nov 2021 17:48 |
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