Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection in d euclidean dimension of a random fractal of dimension DF and a multifractal distribution of probabilities of dimensions Dq (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensions D'q = Dq + DF--d, for a finite interval of q.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada