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Scaling and Scaling-Relevant Dynamical Properties of Penrose Tiling |
| LIU Zhengyou;LIU Youyan;TIAN Decheng2;XIA Haibo1 |
| Department of Physics, South China University of Technology, Guangzhou 510641
1Department of Physics, Wuhan University, Wuhan 430072
2also International Center for Material Physics, Academia Sinica, Shenyang 110015
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| Cite this article: |
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LIU Zhengyou, LIU Youyan, TIAN Decheng et al 1995 Chin. Phys. Lett. 12 98-101 |
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Abstract The scaling and the scaling-relevant spectral properties of Penrose tiling are investigated. The fractal dimension df of this tiling is analytically obtained, which is two, equal to its Euclidean dimension. Similar to usual self-similar structure, the vibrational density of states for Penrose lattice is also found to follow a power law p(ω) ~ωds -1 with spectral dimension ds= 2 , which accounts for a special vibrational excitation in quasicrystals: the fracton-like excitation, whose state is critical. The simulation of random walk on this Penrose lattice indicates that the diffusive dimension dw= 2, thus the relation ds = 2df/dw holds.
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| Keywords:
63.50.+x
63.20.Pw
61.42.+h
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Published: 01 February 1995
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