Entangled polymer complex as Higgs phenomena

TL;DR

This paper develops a topological field theory-based model for entangled polymers, revealing an analogy to the Higgs mechanism in superconductors, and explains the microscopic origin of the tube model in polymer physics.

Contribution

It introduces an effective Maxwell-London equation for entangled polymers, linking topological constraints to the tube model and providing a microscopic foundation for the confining potential.

Findings

Transverse polymer current decays exponentially with a finite penetration depth.

The tube radius corresponds to the decay length of the transverse current.

The probability of tube leakage decreases exponentially with the decay length.

Abstract

We derive an effective Maxwell-London equation for entangled polymer complex under the topological constraint, borrowing the theoretical framework from the topological field theory. We find that the transverse current flux of the test polymer chain, surrounded with entangled chains, decays exponentially from its average position with finite penetration depth, which is analogous to the magnetic-field decay in a superconductor (SC). Like as the mass acquirement of photons in SC is the origin of the magnetic-field decay, the polymer earns uncrossible intersections along the chain due to the preserved linking number, which restricts the deviation of the transverse polymer current in the normal direction. Interestingly, this picture is well incorporated with the most successful phenomenological theory of the so called tube model, of which researchers have long pursued its microscopic origin. The correspondence of our equation of motion to the tube model claims that the confining tube potential is a consequence of the topological constraint (linking number). The tube radius is attributed to the decay length, and increasing the retracting force at intersections or increasing the number of intersections (linking number), the tube becomes narrow and tighter. It further shows that the probability of the tube leakage decays exponentially with the decay length of tube radius.