Anomalous diffusion in ‘‘living polymers’’: A genuine Levy flight?

We have observed anomalously enhanced self- (tracer) diffusion in systems of polymerlike breakable micelles. We argue that it provides the first experimental realization of a random walk for which the second moment of the jump-size distribution fails to exist (``Levy flight''). The basic mechanism is the following: Due to reptation, short micelles diffuse much more rapidly than long ones. As times goes on, shorter and shorter micelles are encountered by the tracer, and hence the effective diffusion constant increases with time.