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

Abstract

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 Lévy 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.

arXiv comment17 pages, 8 figures, Proceedings of the Conference "Small system nonequilibrium fluctuations, dynamics and stochastics, and anomalous behavior", KITPC, Beijing, China

References in corpus (22)

• Intermittent search strategies
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• On the strong anomalous diffusion
• Towards deterministic equations for Levy walks: the fractional material derivative
• Geometry-induced superdiffusion in driven crowded systems
• Lévy walks and scaling in quenched disordered media
• Simple stochastic models showing strong anomalous diffusion
• Rare-event induced binding transition of heteropolymers
• Anomalous diffusion of driven particles in supercooled liquids
• Topological Description of the Aging Dynamics in Simple Glasses
• Rare events and scaling properties in field-induced anomalous dynamics
• Transport and Scaling in Quenched 2D and 3D Lévy Quasicrystals
• On anomalous diffusion and the out of equilibrium response function in one-dimensional models
• Transmission probability through a Lévy glass and comparison with a Lévy walk
• Effect of rare events on out of equilibrium relaxation
• Superdiffusion and Transport in 2d-systems with Lévy Like Quenched Disorder
• Super-diffusion around the rigidity transition: Levy and the Lilliputians
• Fluctuations and correlations of a driven tracer in a hard-core lattice gas
• Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium
• Einstein relation in superdiffusive systems
• Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems

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• Field-induced superdiffusion and dynamical heterogeneity
• Time-dependent active microrheology in dilute colloidal suspensions
• Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas
• Rare Events in Extreme Value Statistics of Jump Processes with Power Tails
• Exact Results for First-Passage-Time Statistics in Biased Quenched Trap Models
• Simulation of the continuous-time random walk using subordination schemes
• Asymmetric discrete random walk and drift-diffusion with unequal jump times, lengths, and probabilities