Published June 2008
| Version Submitted
Journal Article
Open
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
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.
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∗.Attached Files
Submitted - 0705.0338.pdf
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Additional details
Identifiers
- Eprint ID
- 99743
- Resolver ID
- CaltechAUTHORS:20191107-141242740
Related works
- Describes
- https://arxiv.org/abs/0705.0338 (URL)
Funding
- NSF
- DMS-0653720
- NSF
- DMS-0449973
Dates
- Created
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2019-11-08Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field