We investigate the short time and short scale dynamics of membrane phases. The dynamics
of the two point displacement correlator of the membrane is shown to be dominated by the
transverse mean-square displacement of a tagged membrane point and to vary with time t
as∼ t2/3. As a result, the structure factor of oriented lamellar phases at nearly perpendicular
orientations (mean membrane normal parallel to the wavevector k→) decays as a stretched
exponential S (k→, t)∼ e−(Γ kzt) 2/3 with Γkz∼(T/κ) 1/2 (T/η) kz3. For isotropic systems …