Ultradiffusion: the relaxation of hierarchical systems

The authors show that the dynamics of relaxation in hierarchical structures leads to an anomalous decay process which they term ultradiffusion. Using renormalisation group techniques, they explicitly calculate the behaviour of the autocorrelation function in a one-dimensional hierarchical system and show its universal power law decay as a function of temperature. The authors also demonstrate analytically the emergence of a hierarchy of time scales. This phenomenon is relevant to systems ranging from macromolecules to computing structures.