Transport on an annealed disordered lattice

We study the diffusion on an annealed disordered lattice with a local dynamical reorganization of bonds. We show that the typical rearrangement time depends on the renewal rate like $t_r\sim {\tau }^{\alpha }$ with $\alpha \ne 1.$ This implies that the crossover time to normal diffusion in a slow rearrangement regime shows a critical behavior at the percolation threshold. Additional scaling relations for the dependence of the diffusion coefficient on the renewal rate are obtained. The derivation of scaling exponents confirms the crucial role of singly connected bonds in transport properties. These results are checked by numerical simulations in two and three dimensions.