Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics

TL;DR

This paper demonstrates that the phase space trajectories of various anomalous polymer dynamics are well-described by fractional Brownian motion, with systematic deviations observed in certain regimes, advancing understanding of polymer motion.

Contribution

It shows that classical anomalous polymer dynamics are characterized by fractional Brownian motion, providing a unified probabilistic description across different systems.

Findings

Phase space trajectories follow fractional Brownian motion.

Deviations from fBm occur in the transition regime for polymer melts.

The approach unifies the description of diverse polymer dynamics.

Abstract

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.