Novel dimension-independent behaviour for diffusive annihilation on percolation fractals

The authors report the first studies of diffusive annihilation on fractal structures. They find super-universal (d-independent) behaviour for the time decay of the particle density; specifically, for the reaction A+A to 0 they find rho A approximately t-23/, while for the reaction A+B to 0 they find rho A approximately t-13/. A scaling theory for diffusive annihilation is developed that predicts that the first exponent is 1/2ds and the second is 1/4ds, where ds=2df/dw is the spectral dimension. Thus the findings support the Alexander-Orbach conjecture (1982) that ds is independent of d.