DIFFUSION ON LOOPLESS CRITICAL PERCOLATION CLUSTER

In this paper, we calculate the dynamical exponents of diffusion, d(w) /d(f) and d(s), on a percolation cluster at p(c) with no loops, for th e square and simple cubic lattices by the method of spectral analysis of the transition probability matrix. Results show that d, varies sign ificantly with the spatial dimension, unlike in conventional percolati on, but the Alexander-Orbach scaling relation d(s) = 2d(f)/d(w) still holds. Thus it rules out the possibility that this scaling relation fa ils for all loopless fractals because of trapping.