LEVEL STATISTICS FOR ELECTRONIC STATES IN A DISORDERED FRACTAL

We present results for the density of states and the statistics of the energy levels in a random tight binding matrix ensemble defined on a disordered two-dimensional Sierpinski gasket. In the absence of disord er the nearest level spacing distribution function P(S) is shown to fo llow the inverse power law P(S) proportional to S--D0-1, which defines the fractal dimension D-0 = 0.56 +/- 0.01 of the corresponding spectr um. In the random case P(S) approaches, instead, the Poisson law e(-S) , which is consistent with localization of the corresponding eigenstat es. In the presence of a random magnetic flux our results also scale t owards the Poisson statistics.