On 4-point correlation functions in simple polymer models

TL;DR

This paper derives exact formulas for the covariance of Cartesian distances in simple polymer models, revealing persistent correlations and complex effects of interactions, with implications for single-molecule experiments.

Contribution

It provides the first exact covariance formulas for distances in simple polymer models, highlighting non-trivial correlations and interaction effects.

Findings

Correlations exist even without interactions when distances share segments.

Increasing interaction strength does not always increase correlations.

Suggestions for future single-molecule experimental investigations.

Abstract

We derive an exact formula for the covariance of cartesian distances in two simple polymer models, the freely-jointed chain and a discrete flexible model with nearest-neighbor interaction. We show that even in the interaction-free case correlations exist as long as the two distances at least partially share the same segments. For the interacting case, we demonstrate that the naive expectation of increasing correlations with increasing interaction strength only holds in a finite range of values. Some suggestions for future single-molecule experiments are made.