Generalized Langevin equation formulation for anomalous polymer dynamics

For reproducing the anomalous—i.e., sub-diffusive or super-diffusive—behavior in some stochastic dynamical systems, the generalized Langevin equation (GLE) has gained considerable popularity in recent years. Motivated by the question of whether or not a system with anomalous dynamics can have the GLE formulation, here I consider polymer physics, where sub-diffusive behavior is commonplace. I provide an exact derivation of the GLE for phantom Rouse polymers, and by identifying the polymeric response to local strains, I argue the case for a GLE formulation for self-avoiding polymers and polymer translocation through a narrow pore in a membrane. Instances in polymer physics where the anomalous dynamics corresponds to the GLE thus seem to be fairly common.