Winding Angle Distributions for Directed Polymers

Details Winding Angle Distributions for Directed Polymers Winding Angle Distributions for Directed Polymers

1996-10-01

arxiv.org/abs/cond-mat/9610019v1

Physics

Condensed Matter

Statistical Mechanics

31 pages LaTeX and 14 postscript figures

Scientific paper

We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending on whether the interaction is repulsive or neutral, but not on microscopic details. In the presence of a chiral asymmetry, the exponential tails become non universal. In all these cases the mean winding angle is proportional to $\ln t$. When the polymer is confined to a finite region around the winding center, e.g. due to an attractive interaction, the winding angle distribution is Gaussian, with a variance proportional to $t$. We also examine the windings of polymers in random systems. Our results suggest that randomness reduces entanglements, leading to a narrow (Gaussian) distribution with a mean winding angle of the order of $\sqrt{\ln t}$.

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