The Open UniversitySkip to content
 

Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions

Cerovski, V.Z.; Schreiber, M. and Grimm, U. (2005). Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions. Physical Review B, 72(5) 054203.

Full text available as:
[img]
Preview
PDF (Not Set) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (752Kb)
DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1103/PhysRevB.72.054203
Google Scholar: Look up in Google Scholar

Abstract

Spectral properties and anomalous diffusion in the silver-mean (octonacci) quasicrystals in d=1,2,3 are investigated using numerical simulations of the return probability C(t) and the width of the wave packet w(t) for various values of the hopping strength v. In all dimensions we find C(t)~t^(-delta), with results suggesting a crossover from delta<1 to delta=1 when v is varied in d=2,3, which is compatible with the change of the spectral measure from singular continuous to absolute continuous; and we find w(t)~t^beta with 0<beta(v)<1 corresponding to anomalous diffusion. Results strongly suggest that beta(v) is independent of d. The scaling of the inverse participation ratio suggests that states remain delocalized even for very small hopping amplitude v. A study of the dynamics of energy-filtered wave packets in large three-dimensional quasiperiodic structures furthermore reveals that wave packets composed of eigenstates from an interval around the band edge diffuse faster than those composed of eigenstates from an interval of the band-center states: while the former diffuse anomalously, the latter appear to diffuse slower than any power law.

Item Type: Journal Article
ISSN: 1098-0121
Extra Information: Preprint version cond-mat/0407762 available at http://arxiv.org/abs/cond-mat/0407762
---Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.

Some of the symbols and Greek letters may not have transferred correctly into this bibliographic record.
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2219
Depositing User: Uwe Grimm
Date Deposited: 13 Nov 2006
Last Modified: 06 Dec 2010 17:38
URI: http://oro.open.ac.uk/id/eprint/2219
Share this page:

Altmetrics

Scopus Citations

Actions (login may be required)

View Item
Report issue / request change

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk