Dynamic Fluctuations of Semiflexible Filaments

We study both the longitudinal and transverse fluctuations of a semiflexible filament. Using scaling arguments and numerical simulations, we find several regimes for the longitudinal fluctuations which, for short times, scale as $〈\delta r_{\Vert }^2〉\sim t^{7/8}$ and are correlated over a length $l_2\sim t^{1/8}$. Our results are pertinent to experiments on cross-linked filament systems and motor-filament assays. The techniques we develop for the analysis of dynamic correlations should have wide applications in the study of polymer systems.