Random walk and the ideal chain problem on self-similar structures

Random walks and ideal chains (equally weighted trajectories) on self-similar structures are shown to have, in specific examples, drastically different asymptotic behavior. In certain instances localization effects let the end-to-end distance of an ideal chain of length n grow like exp[αlogn${)}^{\phi }$] (φ<1) or (logn${)}^{\psi }$ for large n. The renormalization-group analysis and the fixed point, giving these behaviors, are of a new type. These results could be of experimental relevance for the migration properties of excitations on fractal structures in the presence of a trapping environment.