Title: Transport and scaling in superdiffusive Lévy materials

Abstract:
Transport in strongly heterogeneous and disordered materials can often
be modeled by a Lévy walk, with large fluctuations in step lengths
following Lévy stable laws with algebraic tails.  A key signature of
processes occurring in these materials is that the steps are not
independent, as they are correlated by their mutual positions in the
sample. While uncorrelated Lévy walks are well understood, the
correlation effects, which are expected to exert a deep influence on
the diffusion properties, are still to be characterized.  We consider
correlated Lévy walks on a class of deterministic and random Lévy
structures, modeled on recent experimental settings, with correlation
between steps induced by their geometry. We characterize their
superdiffusive behavior by a "single-long-jump approximation" and a
scaling analysis, which applies to experimentally relevant quantities
such as mean square displacement and transmission probabilities. We
also address the problem of response measurements and fluctuation
relations in these heterogeneous systems.