Colloid diffusion on phospholipid membranes is anomalous

We demonstrate experimentally a simple system in which mean-squared displacement is proportional to time yet the distribution function of displacement probability is exponential, not Gaussian as expected for a classical random walk. This is the case of fluorescent submicron-sized beads that diffuse in one dimension in the smooth potential presented by tubes composed of phospholipid bilayer.~ A discussion of possible physical origins suggests that a family of physical systems whose few degrees of freedom couple to slow environmental fluctuations may behave analogously.