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
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
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.
1995, Vol. 12 
