Hydrodynamics and dynamic fluctuations of fluid membranes

This paper develops a formalism for studying the renormalization of dynamic properties of fluid membranes under coarse graining produced by removal of high-wave-number degrees of freedom. It derives hydrodynamical equations for fluid membranes and shows that appropriately chosen noise sources can lead to a Fokker-Planck equation for the probability distribution that decays to the thermal equilibrium at long times that includes measure factor corrections to the usual Boltzmann weight. Membranes that are incompressible at short length scales are shown, via both static and dynamic renormalization calculations, to be compressible at long length scales. As a result, a flexible membrane will always have a density mode that is distinct from its height or shape mode. Dissipative coefficients in the membrane Rouse model are shown to renormalize whereas those in the Zimm model are shown not to.