Small-world Rouse networks as models of cross-linked polymers

We use the recently introduced small-world networks (SWNs) to model cross-linked polymers, as an extension of the linear Rouse chain. We study the SWN dynamics under the influence of external forces. We focus on the (structurally and thermally averaged) stretching of the SWN, which we determine numerically through diagonalization and analytically using an approximate expression for the SWN density of states. We show that stretching is related to the probability of a random walker over the network to return to its origin. We compare our SWN results to the corresponding ones for Cayley trees.