Entanglement probabilities of polymers: a white noise functional approach

Abstract

The entanglement probabilities for a highly flexible polymer to wind n times around a straight polymer are evaluated using white noise analysis. To introduce the white noise functional approach, the one-dimensional random walk problem is taken as an example. The polymer entanglement scenario, viewed as a random walk on a plane, is then treated and the entanglement probabilities are obtained for a magnetic flux confined along the straight polymer, and a case where an entangled polymer is subjected to the potential V = (s). In the absence of the magnetic flux and the potential V, the entanglement probabilities reduce to a result obtained by Wiegel.