Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces

We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the polymers. In particular, it is shown that for arbitrarily stiff parallel polymers, there is a characteristic separation below which they prefer to bend rather than stay linear. The out-of plane fluctuations of the polymer, screen out the long-range fluctuation-induced forces, resulting in only a short-ranged effective attraction.