Calculation of Spectral Dimension on Inhomogeneous Fractal Lattices

We propose a scheme to derive the spectral dimension of inhomogeneous fractal lattice via renormalization procedure, in which the distribution of masses on the sites of fractals is introduced. The spectral dimension of diamond-type hierarchical lattice and Sierpinski gasket with b = 3 are re-investigated in this way. Moreover, the variants of Sierpinski gaskettype fractals are studied, the results show that the spectral dimension is independent of the details of internal structure of fractal, and thus implies the existence of universality. The source of the universality is also analyzed.