Levy Flights in Inhomogeneous Media

Abstract

We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Levy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Levy index $\mu$. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.

4 pages, 4 figures

References in corpus (4)

• Fluid Particle Accelerations in Fully Developed Turbulence
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Levy Flights in External Force Fields: From Models to Equations
• Levy flights in quenched random force fields

Cited by in corpus (49)

• The scaling laws of human travel
• Saving Human Lives: What Complexity Science and Information Systems can Contribute
• Time-space fabric underlying anomalous diffusion
• Perspective: Ultrafast magnetism and THz spintronics
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Lévy flights in a steep potential well
• From subdiffusion to superdiffusion of particles on solid surfaces
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Fractional Fokker-Planck equation for Lévy flights in nonhomogeneous environments
• Multiplicative Lévy processes: Itô versus Stratonovich interpretation
• Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
• Fluctuation-driven directed transport in the presence of Levy flights
• Diffusion equations for a Markovian jumping process
• Negative superdiffusion due to the inhomogeneous convection
• Mesoscopic description of reactions under anomalous diffusion: A case study
• Particle Dispersion on Rapidly Folding Random Hetero-Polymers
• Optimization and universality of Brownian search in quenched heterogeneous media
• Lévy-walk-like Langevin dynamics
• Nonlinear stochastic equations with multiplicative Lévy noise
• Non-Markovian Levy diffusion in nonhomogeneous media
• Levy flights in confining potentials
• Superdiffusion and Transport in 2d-systems with Lévy Like Quenched Disorder
• Contact processes with long-range interactions
• Epidemic spreading with long-range infections and incubation times
• Anomalous diffusion in systems driven by the stable Levy noise with a finite noise relaxation time and inertia
• Lévy flights in inhomogeneous environments
• Radiation trapping and Lévy flights in atomic vapours: an introductory review
• Accelerating random walks by disorder
• Langevin dynamics for Lévy walk with memory
• Multiplicative Levy noise in bistable systems
• Levy targeting and the principle of detailed balance
• Continuous time multidimensional Markovian description of Levy walks
• Lévy flights in inhomogeneous environments and 1/f noise
• Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media
• Catalytic reactions with bulk-mediated excursions: Mixing fails to restore chemical equilibrium
• Universality in the Onset of Super-Diffusion in Lévy Walks
• Self-organized transient facilitated atomic transport in Pt/Al(111)
• Testing Short Distance Anisotropy in Space
• Levy walks with variable waiting time: a ballistic case
• Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
• Competition between ac driving-forces and Lévy flights in a nonthermal ratchet
• Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps
• Asymmetric Levy flights in nonhomogeneous environments
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle
• Levy flights in confining environments: Random paths and their statistics
• Origin of universality in the onset of superdiffusion in Lévy walks
• Mesoscopic Fractional Quantum in Soft Matter
• A maximal $L_p$-regularity theory to initial value problems with time measurable nonlocal operators generated by additive processes