Winding Angle Distributions for Random Walks and Flux Lines

摘要

We study analytically and numerically the winding of a flux line around acolumnar defect. Reflecting and absorbing boundary conditions apply to marginalor repulsive defects, respectively. In both cases, the winding angledistribution decays exponentially for large angles, with a decay constantdepending only on the boundary condition, but not on microscopic features. New{\it non-universal} distributions are encountered for {\it chiral} defectswhich preferentially twist the flux line in one direction. The resultingasymmetric distributions have decay constants that depend on the degree ofchirality. In particular, strong chirality encourages entanglements and leadsto broad distributions. We also examine the windings of flux lines in thepresence of point impurities (random bonds). Our results suggest that pinningto impurities reduces entanglements, leading to a narrow (Gaussian)distribution.