Fractional Kramers Equation

By Eli Barkai, R. Silbey. 2000

151 citations recorded by the source corpus.

We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external nonlinear force field. For the force-free case, the velocity damping follows the Mittag−L...

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a534a04416eef1f79c6bcaba02201b0649a370c9

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Citations in the corpus

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “Equation (20) is equivalent to the integral transformation (Barkai and Silbey 2000), P(x, t) = ∫ ∞ 0 dsEα(s, t)PM(x, s) (22) which corresponds to a generalized Laplace transformation from t to ηα η1 uα .”
An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations (2003, unknown): “Another route to solving fractional equations is through the integration of the product of the solution of the corresponding nonfractional equation (the Brownian counterpart obtained by setting γ → 1) and a one-sided Lévy stable density [4, 17].”
L\'evy walks (2014, background): “…Fokker-Planck (Barkai, 2001; Barkai et al., 2000b; Chechkin et al., 2003; Heinsalu et al., 2007; Metzler et al., 1999) and Klein-Kramers equations (Barkai and Silbey, 2000; Dieterich et al., 2008; Eule et al., 2007; Friedrich 20 et al., 2006a; Metzler and Sokolov, 2002), and it remains an active…”
The Role of Fractional Time-Derivative Operators on Anomalous Diffusion (2017, background): “It is worth mentioning that crossovers between diffusive regimes can also be described by generalized Langevin equations [67] and fractional (with the Riemann-Liouville operator) Kramers equations [19], among other approaches [68, 69].”