Scaling properties of field-induced superdiffusion in Continous Time Random Walks

R. Burioni 1, 2 G. Gradenigo 3, 4 A. Sarracino 3 A. Vezzani 5, 6 A. Vulpiani 7

Small system nonequilibrium fluctuations, dynamics and stochastics, and anomalous behavior, China. 62, pp.514, 2014, Communications in Theoretical Physics

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.

  • 1. Fisica
  • 2. INFN
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 4. CEA - CEA Saclay
  • 5. Fisica
  • 6. Fisica
  • 7. INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]