Stretching of a fractal polymer around a disc reveals KPZ-like statistics

TL;DR

This study reveals that the conformational statistics of a fractal polymer stretched around a curved surface exhibit KPZ universality, with curvature inducing KPZ-like scaling laws regardless of the polymer's fractal dimension.

Contribution

The paper demonstrates that curvature induces KPZ-like statistical behavior in stretched fractal polymers, revealing universal scaling laws independent of fractal dimension.

Findings

Polymer excursions scale as R^{1/3} with curvature radius R.

Correlation length scales as R^{2/3}, matching KPZ dynamic exponent.

Curvature induces universal KPZ-like statistics in polymer conformations.

Abstract

While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. Here by means of the scaling analyses and computer simulations we examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius $R$. Surprisingly, we reveal that the typical excursions of the polymer away from the surface scale as $\Delta \sim R^{\beta}$, with the Kardar-Parisi-Zhang (KPZ) growth exponent $\beta=1/3$, for any fractal dimension of the chain. Moreover, we find that the curvature-induced correlation length of a fractal chain behaves as $S^* \sim R^{1/z}$ with the KPZ dynamic exponent $z=3/2$, suggesting that the crossover from flat to curved geometry of a stretched polymer corresponds to the crossover from large to short time scales in the KPZ stochastic growth. Thus, we argue that curvature of an underlying boundary furnishes universal KPZ-like statistics to the stretched fractal paths, which further suggests numerous connections with several branches of mathematical physics.