Paradoxal Diffusion in Chemical Space for Nearest-Neighbor Walks over Polymer Chains

We consider random walks over polymer chains (modeled as simple random walks or self-avoiding walks) and allow from each polymer site jumps to all Euclidean (not necessarily chemical) neighboring sites. For frozen chain configurations the distribution of displacements (DD) of a walker along the chain shows a paradoxal behavior: The DD's width (interquartile distance) grows with time as $\Lambda \propto t^{\alpha }$, with $\alpha \approx 0.5$, but the DD displays large power-law tails. For annealed configurations the DD is a Lévy distribution and its width is strongly superdiffusive.