Generalized Langevin Equation Formulation for Anomalous Polymer Dynamics

TL;DR

This paper investigates the applicability of the Generalized Langevin Equation (GLE) to model anomalous polymer dynamics, providing exact derivations for certain polymer types and arguing for its broader relevance in polymer physics.

Contribution

It offers the first exact derivation of the GLE for phantom Rouse polymers and extends the argument for GLE applicability to self-avoiding polymers and polymer translocation.

Findings

Exact GLE derivation for phantom Rouse polymers

Support for GLE formulation in self-avoiding polymers

Application of GLE to polymer translocation processes

Abstract

For reproducing the anomalous -- i.e., sub- 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 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, andby identifying polymeric response to local strains, I argue the case for the GLE formulation for self-avoiding polymers and polymer translocation through a narrow pore in a membrane. The number of instances in polymer physics, where the anomalous dynamics corresponds to the GLE, thus seems to be fairly common.