Power-law energy level spacing distributions in fractals

In this paper we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy level distribution of a fractal follows a power-law behavior, if its energy spectrum is a limit set of piecewise linear functions. We propose that such a behavior is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behavior of the energy level spacing distributions are proposed.