Novel dimension-independent behaviour for diffusive annihilation on percolation fractals

Abstract

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 ¹/₂d_s and the second is ¹/₄d_s, where d_s=2d_f/d_w is the spectral dimension. Thus the findings support the Alexander-Orbach conjecture (1982) that d_s is independent of d.