Dynamical fluctuations of spherically closed fluid membranes

Properties of dynamical shape fluctuations of spherically closed fluid membranes such as vesicles or microemulsion droplets are discussed. As a boundary condition at the interface, we employ the generalized Laplace's formula obtained by Zhong-can and Helfrich. We calculate the oscillation frequencies and the relaxation times of the membranes for a small deformation under the constraint of either constant area or constant volume. Furthermore, the diffusion coefficient of the droplet is estimated from the translational sideways mode. Our result does not depend on the form of the shape energy, in agreement with the recent prediction by Edwards and Schwartz.