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

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 $S^{\ast }\sim R^{1/z}$ 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.

References in corpus (12)

• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• Rheology of Ring Polymer Melts: From Linear Contaminants to Ring/Linear Blends
• Exact distribution of the maximal height of p vicious walkers
• Constrained Brownian motion: Fluctuations away from circular and parabolic barriers
• Geometrical optics of constrained Brownian motion: three short stories
• Geometrical optics of constrained Brownian excursion: from the KPZ scaling to dynamical phase transitions
• Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime
• Many-body contacts in fractal polymer chains and fBm trajectories
• Native ultrametricity of sparse random ensembles
• Brownian flights over a circle
• Fixman problem revisited: When fluctuations of inflated ideal polymer loop are non-Gaussian?

Cited by in corpus (1)

• Non-algebraic first return probability of a stretched random walk near a convex boundary and its effect on adsorption