Superdiffusion and Transport in 2d-systems with Lévy Like Quenched Disorder

Abstract

We present an extensive analysis of transport properties in superdiffusive two dimensional quenched random media, obtained by packing disks with radii distributed according to a Lévy law. We consider transport and scaling properties in samples packed with two different procedures, at fixed filling fraction and at self-similar packing, and we clarify the role of the two procedures in the superdiffusive effects. Using the behavior of the filling fraction in finite size systems as the main geometrical parameter, we define an effective Lévy exponents that correctly estimate the finite size effects. The effective Lévy exponent rules the dynamical scaling of the main transport properties and identify the region where superdiffusive effects can be detected.

12 pages, 19 figures

References in corpus (2)

• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Holey Random Walks: Optics of Heterogeneous Turbid Composites

Cited by in corpus (18)

• Light in correlated disordered media
• The Single Big Jump Principle in Physical Modelling
• Splitting of the universality class of anomalous transport in crowded media
• Rare events in generalized Lévy Walks and the Big Jump principle
• Splitting Probabilities of Jump Processes
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Lévy processes on a generalized fractal comb
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Scaling properties of field-induced superdiffusion in Continous Time Random Walks
• Steering random walks with kicked ultracold atoms
• Rare events in stochastic processes with sub-exponential distributions and the Big Jump principle
• Walk dimension for light in complex disordered media
• Anomalous transmission and drifts in one-dimensional Levy structures
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
• Leftward, Rightward and Complete Exit Time Distributions of Jump Processes
• Run-and-tumble particles in slit geometry as a splitting probability problem
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables