Anomalous motion of membranes under a localized external potential

We investigate the relaxation and autocorrelation function of a particle attached to a membrane under the combined influence of an external potential and of the thermal undulations provided by the membrane. For a harmonic external potential the mean relaxation is given by the Mittag-Leffler decay function, while the autocorrelation, although closely related to the Mittag-Leffler behaviour, displays a more complex pattern. Relationship to experiments using optical tweezers is discussed.