Non-homogeneous persistent random walks and averaged environment for the Lévy-Lorentz gas

Abstract

We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the Lévy-Lorentz gas, namely a 1-d model characterized by a fat polynomial tail of the distribution of scatterers' distance, with parameter $\alpha$. By varying the value of $\alpha$ we have a transition from normal transport to superdiffusion, which we characterize by appropriate continuum limits.

arXiv comment11 pages, 3 figures

References in corpus (11)

• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• On the strong anomalous diffusion
• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• The Single Big Jump Principle in Physical Modelling
• One-Dimensional Stochastic Lévy-Lorentz Gas
• Lévy walks and scaling in quenched disordered media
• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Isothermal Langevin dynamics in systems with power-law spatially-dependent friction
• A continuous-time persistent random walk model for flocking
• Random walks in a one-dimensional Lévy random environment
• Fokker-Planck equation with memory: the crossover from ballistic to diffusive processes in many-particle systems and incompressible media

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