2007/06/28 by Ihor Lubashevsky, Lubashevsky, Ihor, R. Friedrich +4
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #Diffusion and Search Dynamics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0706.4320
paper of 5 pages with 3 figures with added supplementary materials
arxiv created 2007/06/28 · openalex publication_date 2007/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On the basis of multivariate Langevin processes we present a realization of Levy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Levy flights. Our procedure is similar to the treatment of the Kramers-Fokker Planck equation in the Smoluchowski limit. The proposed approach forms a feasible way of tackling Levy flights in inhomogeneous media or systems with boundaries what is up to now a challenging problem.