Generalized Langevin equation for a tagged monomer in a Gaussian semiflexible polymer

In this study, we present a comprehensive analysis of the motion of a tagged monomer within a Gaussian semiflexible polymer model. We carefully derived the generalized Langevin equation (GLE) that governs the motion of a tagged central monomer. This derivation involves integrating out all the other degrees of freedom within the polymer chain, thereby yielding an effective description of the viscoelastic motion of the tagged monomer. A critical component of our analysis is the memory kernel that appears in the GLE. By examining this kernel, we characterized the impact of bending rigidity on the non-Markovian diffusion dynamics of the tagged monomer. Furthermore, we calculated the mean-squared displacement of the tagged monomer using the derived GLE. Our theoretical findings were corroborated by the Langevin dynamics simulation and scaling theory. Our results not only show remarkable agreement with previously known results in certain limiting cases but also provide dynamic features over the entire timescale.