Self-reptation and slow topological time scale of knotted polymers

We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale, and show that it is related to a self-reptation of the knotted region. The associated dynamical exponent, $z_T=2.32\pm .1$, can be related to that of the equilibrium knot length distribution and determines the behaviour of several dynamical quantities.