Langevin Approach to Levy Flights in Fixed Potentials: Exact Results for Stationary Probability Distributions - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: The functional method to derive the fractional Fokker-Planck equation forprobability distribution from the Langevin equation with Levy stable noise isproposed. For the Cauchy stable noise we obtain the exact stationaryprobability density function of Levy flights in different smooth potentialprofiles. We find confinement of the particle in the superdiffusion motion witha bimodal stationary distribution for all the anharmonic symmetric monostablepotentials investigated. The stationary probability density functions showpower-law tails, which ensure finiteness of the variance. By reviewing recentresults on these statistical characteristics, the peculiarities of Levy flightsin comparison with ordinary Brownian motion are discussed.



Author: A. A. Dubkov, B. Spagnolo

Source: https://arxiv.org/



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