Dynamics of two topologically entangled chains

TL;DR

This paper extends topological field theories, like the BF model, to describe the dynamic behavior of entangled polymers, linking topological invariants with polymer motion over time.

Contribution

It introduces a generalized BF model framework that captures the evolving topology of polymer chains during their dynamics.

Findings

The generalized model successfully describes polymer entanglement dynamics.

It connects topological invariants with real-time polymer shape changes.

The approach offers a new perspective on polymer statistical mechanics.

Abstract

Starting from a given topological invariant, we argue that it is possible to construct a topological field theory with a finite number of Feynman diagrams and an amplitude of gauge invariant objects that is a function of that invariant. This is for example the case of the Gauss linking number and of the abelian BF models which has been already successfully applied in the statistical mechanics of polymers. In this work it is shown that a suitable generalization of the BF model can be applied also to polymer dynamics, where the polymer trajectories are not static, but change their shape during time.