VIBRATION SPECTRUM AND SPECTRAL DIMENSION OF ONE-DIMENSIONAL COMPLEX PENROSE CHAIN

The vibration spectrum and the scaling exponents near zero frequency are calculated for me-dimensional complex Penrose chain which is constituted with two kinds of atoms and without any periodic structure. The results show that there are obviously several gape. The scaling exponent of frequence, defined by ω(bN) ~ b^-a_ω(N), equals one. The Penrose chain is a nontrivial fractal with the inhomogeneous and selfsimilar structure, the fractal and spectral dimensions me all equal to one.