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Abstract |
Can intrinsic curvature of the space yield a similar regime of fluctuations as a
certain type of random potentials? In this talk by means of scaling analyses of
the free energy and computer simulations I will discuss stretching of a fractal
polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. The typical
excursions of the polymer away from the surface scale as $\Delta \sim
R^{\beta}$, with the Kardar-Parisi-Zhang (KPZ) growth exponent $\beta=1/3$ and
the curvature-induced correlation length is described by the KPZ exponent z=3/2.
Remarkably, the uncovered KPZ scaling is independent of the fractal dimension of
the polymer and, thus, is universal across the classical polymer models, e.g.
SAW, randomly-branching polymers, crumpled unknotted rings. The one-point
distribution of fluctuations, as found in simulations, can be well described by
the squared Airy law, connecting our 2D polymer problem with the (1+1)D Ferrari-
Spohn universality class of constrained random walks. A relation between
directed polymers in quenched random potential (KPZ) and stretched polymers
above the semicircle will be explained. |
