Relaxation of a Single Knotted Ring Polymer
Abstract
The relaxation of a single knotted ring polymer is studied by Brownian dynamics simulations. The relaxation rate lambdaq for the wave number q is estimated by the least square fit of the equilibrium time-displaced correlation function to a double exponential decay at long times. The relaxation rate distribution of a single ring polymer with the trefoil knot appears to behave as lambdaq=A(1/N)x for q=1 and lambdaq=A'(q/N)x' for q=2 and 3, where x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for each N is given by q=2 for small values of N, while it is given by q=1 for large values of N. This crossover corresponds to the change of the structure of the ring polymer caused by the localization of the knotted part to a part of the ring polymer.