Large scale behavior of semiflexible heteropolymers

TL;DR

This paper analyzes a discrete model of heterogeneous semiflexible polymers, demonstrating that despite local differences, the chains exhibit Brownian behavior on large scales and providing explicit diffusion constants.

Contribution

It introduces a novel analysis of a heterogeneous semiflexible polymer model using tensor and Fourier analysis, establishing large-scale Brownian behavior and mixing conditions.

Findings

Large-scale Brownian behavior of the polymer model

Explicit expression for the diffusion constant

Conditions for quantitative mixing properties

Abstract

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a Brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative Fourier analysis, we establish the Brownian character of the model on large scale and we obtain an expression for the diffusion constant. We moreover give conditions yielding quantitative mixing properties.