  We characterize the fluctuation properties of a polymer chain under external
tension and the fluctuation-induced forces between two ring molecules threaded
around the chain. The problem is relevant in the context of fluctuation-induced
forces in soft matter systems, features of liquid interfaces and to describe
properties of polyrotaxanes and slide-ring materials. We perform molecular
dynamics simulations of the Kremer-Grest bead-spring model for the polymer and
a simple ring-molecule model, in the canonical ensemble. We study transverse
fluctuations of the stretched chain, as a function of chain stretching and in
the presence of ring-shaped threaded molecules. The fluctuation spectra of the
chains are analyzed in equilibrium at constant temperature and the differences
in presence of two ring molecules are compared. For the rings located at fixed
distances, we find an attractive fluctuation-induced force between the rings,
proportional to the temperature and decaying with the ring distance. We
characterize this force as a function of ring distance, chain stretching, ring
radius and measure the differences between the free chain spectrum and the
fluctuations of the chain constrained by the rings. We also compare the
dependence and range of the force found in the simulations with theoretical
models coming from different fields.
