Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics

It has been recently shown that the phase space trajectories for the anomalous dynamics of a tagged monomer of a polymer --- for single polymeric systems such as phantom Rouse, self-avoiding Rouse, Zimm, reptation, and translocation through a narrow pore in a membrane; as well as for many-polymeric system such as polymer melts in the entangled regime --- is robustly described by the Generalized Langevin Equation (GLE). Here I show that the probability distribution of phase space trajectories for all these classical anomalous dynamics for single polymers is that of a fractional Brownian motion (fBm), while the dynamics for polymer melts between the entangled regime and the eventual diffusive regime exhibits small, but systematic deviations from that of a fBm.