Quantum intermittency : old or new phenomenon ?

Abstract
Two seemingly unrelated themes in the research of Giovanni Paladin have been the thermodynamical formalism for fractal measures, and abstract models to account for the structure of well-developed turbulence. Here, intermittent behaviour seems to be the deep origin of the non-K41 scaling relations characterizing velocity differences in the flow. These themes-multifractal properties (of certain spectral measures) and non-trivial scaling functions (of localization properties in time)-turn out to be intimately related in the description of wave propagation in almost periodic systems, classical and quantum. Their relations lead to what I call the phenomenon of quantum intermittency : I develop a complete analytical treatment of its appearance in the motion generated by Hamiltonians associated with Julia set measures.