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. 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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/s00220-008-0451-3	DOI	Article
https://rdcu.be/bWoFi	Publisher	Free ReadCube access
https://arxiv.org/abs/0705.0338	arXiv	Discussion Paper

ORCID:

Author	ORCID
Damanik, David	0000-0001-5924-3849

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∗.

Funders:

Funding Agency	Grant Number
NSF	DMS-0653720
NSF	DMS-0449973

Subject Keywords:

Fractal Dimension; Hausdorff Dimension; Transfer Matrice; Singular Continuous Spectrum; Periodic Spectrum

Issue or Number:

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

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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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