Levy Flights in External Force Fields: From Models to Equations
arXiv:cond-mat/0210387 · doi:10.1016/S0301-0104(02)00671-7
Abstract
We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy statistics can emerge from the fractal temporal nature of the underlying process, i.e. a high variability in the rate of microscopic events. On the other hand, they may be a direct consequence of the scale-free spatial structure on which the process evolves. Although both forms considered lead to Boltzmann equilibrium, the relaxation patterns are quite different. As an example, generalized diffusion in a double-well potential is considered.
21 pages, 5 figures
References in corpus (3)
Cited by in corpus (47)
- Levy Flights, Non-local Search and Simulated Annealing
- Levy Flight Superdiffusion: An Introduction
- Levy Flights in Inhomogeneous Media
- Generalized Fokker-Planck equation: Derivation and exact solutions
- Codifference as a practical tool to measure interdependence
- Stationary states in Langevin dynamics under asymmetric Lévy noises
- Cooling down Levy flights
- Non-equilibrium Phase Transitions with Long-Range Interactions
- Transport in a Levy ratchet: Group velocity and distribution spread
- Steady-State Lévy Flights in a Confined Domain
- Fluctuation-driven directed transport in the presence of Levy flights
- Particle Dispersion on Rapidly Folding Random Hetero-Polymers
- Stationary states in single-well potentials under symmetric Levy noises
- Langevin equation with super-heavy-tailed noise
- Levy stable distributions via associated integral transform
- Levy flights and nonlocal quantum dynamics
- Levy flights in confining potentials
- Parameters of the fractional Fokker-Planck equation
- Epidemic spreading with long-range infections and incubation times
- Lévy flights in inhomogeneous environments
- Accelerating random walks by disorder
- Hopping Models of Charge Transfer in a Complex Environment: New Class of Coupled Memory Continous-Time Random Walks
- 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
- Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise
- Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems
- Bimodality and hysteresis in systems driven by confined Lévy flights
- Multimodal stationary states under Cauchy noise
- Stochastic dynamics and the predictability of big hits in online videos
- Peculiarities of escape kinetics in the presence of athermal noises
- Escape from the potential well: competition between long jumps and long waiting times
- Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
- Defect-related Anomalous Mobility of Small polarons in Oxides: the Case of Congruent Lithium Niobate
- Probability distribution function for systems driven by superheavy-tailed noise
- Stationary states for underdamped anharmonic oscillators driven by Cauchy noise
- Heavy-tailed targets and (ab)normal asymptotics in diffusive motion
- Anomalous Diffusion in Velocity Space
- A compounded random walk for space-fractional diffusion on finite domains
- Nonlinear friction in underdamped anharmonic stochastic oscillators
- 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
- Stochastic kinetics under combined action of two noise sources
- Thermalization of Levy flights: Path-wise picture in 2D
- How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme
- Drifted escape from the finite interval
- Deterministic force-free resonant activation