HYDRODYNAMICS AND DYNAMIC FLUCTUATIONS OF FLUID MEMBRANES

This paper develops a formalism for studying the renormalization of dy namic properties of fluid membranes under coarse graining produced by removal of high-wave-number degrees of freedom. It derives hydrodynami cal 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 tha t includes measure factor corrections to the usual Boltzmann weight. M embranes that are incompressible at short length scales are shown, via both static and dynamic renormalization calculations, to be compressi ble at long length scales. As a result, a flexible membrane will alway s have a density mode that is distinct from its height or shape mode. Dissipative coefficients in the membrane Rouse model are shown to reno rmalize whereas those in the Zimm model are shown not to.